Structure that breaks InChI
Okay, let's tackle at least one problem here. Consider the rotation of 1,2-dichloroethane (BP86/cc-pVDZ):
 

These conformational changes can be further rationalised:


C and C' are the same conformation, since these are mirror images. 
The same applies to B and B'.
A and C are local minima and can be referred to as conformes in the above given way
B and D are transition states - they are not stable.
If you consider the rotation A to C as a reaction, this state would mark the maximum energy needed for the conversion. I believe with reactions it is meant, that an accurate description of the transition state by InChI is not possible.




For the term non-local chirality I suggest you look at BINAP or BINOL.

In this case I have used a slightly abridged version of BINAP for educational purposes, where $\ce{Ph -&gt; Me}$.  

  

Other wonderful examples of non-local chirality include helicenes, which have helical chirality. Here is one example of a fancy azonia derivative of hexahelicene (parent compound and links). The structure is available at the Cambridge Crystallographic Data Centre (CCDC) Database. I removed the anion and converted it to xyz coordinates which I include in the appendix. Here are the structures, left P-chirality, right M-chirality:

  

On another account of non/local chirality, there is the planar chirality, as can be seen in trans-Cyclooctene (the bottom two). For further reading I suggest Neuenschwander et.al. "The Conformations of Cyclooctene: Consequences for Epoxidation Chemistry."




Markush Structures are a kind of summary structure for certain compound classes. A very simple example would be a monosubstituted biphenyl system, where the upper structure is a representation of all three below. However, it is noteworthy, that each instance of a Markush structure can be well explained by InChI.

More complicated structures are often used in patents and in other scientific publications, usually specifically referring to a very general procedure or mechanism. I found one on wikipedia commons, that could well represent a million molecules:




And another way to break the InChI are clusters. Although the definition is not very specific, the $\ce{[KO{}^{\mathit{t}}Bu]_4}$ tetramer (wikipedia, chemspider) certainly contains one. While the monomer can be described via InChI, the tetra- or Polymer should fail. It was published by Chisholm et.al. in Polyhedron and the *.cif file can be obtained from CCDB. I cleaned it up a little bit and included the *.xyz in the appendix. You can quite nicely see the $\ce{K4}$ tetrahedral cluster in the middle (hydrogens omitted for clarity). 




Last but not least, I'd like to cover the matter of complicated organometallic molecules. As such I'd like to introduce the Grubbs' catalysts. Grubbs obtained the Nobel Prize in Chemistry 2005 for his research in conjunction with Yves Chauvin and Richard R. Schrock. One of the key publications was "Ring-opening metathesis polymerization (ROMP) of norbornene by a Group VIII carbene complex in protic media". The crystal structure can also be obtained at CCDC. Another example stems from "Synthesis and Applications of $\ce{RuCl2(=CHR')(PR3)2}$:  The Influence of the Alkylidene Moiety on Metathesis Activity" and is also available via CCDC. This structure can also be found in the appendix. It is generally known as a 1st generation Grubbs catalyst (Hydrogens omitted for clarity).




Appendix

The following section contains the nuclear coordinates in *.xyz(XMol) file format and angstroms as unit. (If not denoted otherwise, structures are obtained at BP86/cc-pVDZ.)

1,2-dichloroethane A  

C        0.000000000      0.000000000      0.000000000
C        0.000000000      0.000000000      1.521307000
Cl       1.723641000      0.000000000     -0.593797000
H       -0.486731000     -0.904743000     -0.410753000
H       -0.486731000      0.904743000     -0.410753000
Cl      -1.723641000      0.000000000      2.115104000
H        0.486731000     -0.904743000      1.932060000
H        0.486731000      0.904743000      1.932060000


1,2-dichloroethane B  

C        0.030242000      0.085780000     -0.007620000
C       -0.030242000      0.085780000      1.528927000
Cl       1.518312000     -0.758527000     -0.631286000
H       -0.837191000     -0.442465000     -0.444148000
H        0.070555000      1.115212000     -0.412109000
Cl      -1.518312000     -0.758527000      2.152593000
H        0.837191000     -0.442465000      1.965455000
H       -0.070555000      1.115212000      1.933416000


1,2-dichloroethane C

C        0.066377000      0.127741000      0.004558000
C       -0.066377000      0.127741000      1.516749000
Cl       1.083384000     -1.241726000     -0.615213000
H       -0.919786000      0.050600000     -0.492443000
H        0.568277000      1.063384000     -0.317636000
Cl      -1.083384000     -1.241726000      2.136520000
H        0.919786000      0.050600000      2.013750000
H       -0.568277000      1.063384000      1.838943000


1,2-dichloroethane D

C        0.164887000      0.141535000     -0.000240000
C       -0.164887000      0.141535000      1.521547000
Cl       0.337146000     -1.473219000     -0.795160000
H       -0.633932000      0.666019000     -0.558099000
H        1.123149000      0.665665000     -0.177529000
Cl      -0.337146000     -1.473219000      2.316468000
H        0.633932000      0.666019000      2.079406000
H       -1.123149000      0.665665000      1.698836000


R-BINAP

C       -0.086423000     -0.055821000     -0.031546000
C       -0.090885000     -0.047699000      1.480085000
C        1.148913000     -0.158515000      2.237313000
C        1.064686000     -0.139089000      3.676951000
C       -0.131097000     -0.014450000      4.357670000
C       -1.357362000      0.116010000      3.652970000
C       -1.345263000      0.107319000      2.211098000
P        2.768926000     -0.321256000      1.451350000
H        1.988600000     -0.233144000      4.265654000
H       -0.135982000     -0.008251000      5.459401000
C       -2.590782000      0.269421000      4.370415000
C       -2.623021000      0.305506000      1.559779000
C        0.437392000      1.073619000     -0.788457000
C        0.410661000      0.991852000     -2.228054000
C       -0.079670000     -0.105834000     -2.908992000
C       -0.579162000     -1.233570000     -2.204534000
C       -0.579999000     -1.219208000     -0.762676000
P        1.107602000      2.557133000     -0.001640000
H        0.790955000      1.839345000     -2.816335000
H       -0.077540000     -0.112552000     -4.010726000
C       -1.063317000     -2.378355000     -2.921905000
C       -1.047368000     -2.424579000     -0.111239000
C       -3.792005000      0.431032000      3.705083000
H       -2.558632000      0.263827000      5.471798000
H       -4.735477000      0.552772000      4.258523000
C       -3.797353000      0.457087000      2.279022000
H       -2.662047000      0.340912000      0.466043000
H       -4.750761000      0.602046000      1.748556000
C       -1.503463000     -3.517255000     -0.830391000
H       -1.036094000     -2.475958000      0.982488000
H       -1.854657000     -4.415344000     -0.299810000
C       -1.523650000     -3.499569000     -2.256520000
H       -1.052652000     -2.347534000     -4.023279000
H       -1.890198000     -4.377463000     -2.809877000
C        4.061075000     -0.509159000      2.730645000
C        2.844045000     -1.846744000      0.446017000
C        1.585856000      3.772639000     -1.280334000
C       -0.173490000      3.383258000      1.008127000
H        0.254332000      4.289560000      1.485098000
H       -1.067700000      3.703930000      0.418133000
H       -0.532498000      2.717241000      1.815764000
H        1.997887000      4.670081000     -0.777298000
H        2.377005000      3.362349000     -1.938832000
H        0.749130000      4.118465000     -1.941170000
H        5.044249000     -0.601334000      2.227532000
H        4.100503000      0.383637000      3.385840000
H        3.944572000     -1.404262000      3.395364000
H        3.842692000     -1.931312000     -0.030903000
H        2.674387000     -2.779210000      1.039384000
H        2.087489000     -1.826871000     -0.361580000


S-BINAP

C       -1.383946000     -3.448543000     -2.256996000
C       -1.065989000     -2.266144000     -2.910129000
C       -0.652376000     -1.110469000     -2.179491000
C       -0.563545000     -1.177237000     -0.738280000
C       -0.899026000     -2.413534000     -0.098700000
C       -1.299620000     -3.519323000     -0.838209000
C       -0.154302000     -0.008671000      0.004167000
C        0.166467000      1.182512000     -0.673969000
C        0.072046000      1.221328000     -2.098779000
C       -0.323252000      0.113168000     -2.831301000
C       -0.061735000     -0.093981000      1.507135000
C       -1.110430000      0.372113000      2.322674000
C       -0.989013000      0.267385000      3.742090000
C        0.132224000     -0.289631000      4.336601000
C        1.210137000     -0.777916000      3.542877000
C        1.113248000     -0.682564000      2.103804000
C        2.206553000     -1.174312000      1.320794000
C        3.329975000     -1.726929000      1.922868000
C        3.419059000     -1.820539000      3.340084000
C        2.377998000     -1.353835000      4.130094000
P       -2.590653000      1.186493000      1.502738000
C       -3.750658000     -0.293139000      1.402088000
P        0.636241000      2.692004000      0.339668000
C        2.511918000      2.555623000      0.253510000
C       -3.385046000      2.079953000      2.947654000
C        0.388676000      4.078351000     -0.898992000
H       -1.802841000      0.635802000      4.383638000
H        0.202504000     -0.360978000      5.434128000
H        0.319305000      2.150696000     -2.632672000
H       -0.386992000      0.166196000     -3.930250000
H        2.436377000     -1.419019000      5.228476000
H        4.313241000     -2.262708000      3.805535000
H        2.146133000     -1.110484000      0.224695000
H        4.157224000     -2.097887000      1.298347000
H       -0.834575000     -2.478936000      0.997042000
H       -1.552289000     -4.458551000     -0.322477000
H       -1.128190000     -2.199481000     -4.008215000
H       -1.700498000     -4.331984000     -2.832408000
H        2.950535000      3.473538000      0.698290000
H        2.842563000      1.687658000      0.858736000
H        2.884117000      2.439555000     -0.786611000
H        0.678948000      5.023670000     -0.395042000
H        0.990357000      3.982867000     -1.828352000
H       -0.686746000      4.150262000     -1.160750000
H       -4.302108000      2.573768000      2.564446000
H       -3.673500000      1.421270000      3.794842000
H       -2.700063000      2.872570000      3.312044000
H       -4.742112000      0.063129000      1.051704000
H       -3.359638000     -1.014277000      0.656570000
H       -3.871382000     -0.807607000      2.379049000


M-8a-azonia[6]helicene (from crystal structure)

N        3.565811000      0.259443000     13.724558000
C        7.445232000     -1.196589000     12.564039000
C        8.629416000     -1.762757000     12.151335000
C        8.885324000     -1.978555000     10.783139000
C        7.914184000     -1.694865000      9.864763000
C        6.665024000     -1.171130000     10.265448000
C        5.584378000     -1.088690000      9.330104000
C        4.339207000     -0.800151000      9.738213000
C        4.088732000     -0.406137000     11.083608000
C        2.763235000     -0.187914000     11.543327000
C        2.522579000      0.029096000     12.830042000
C        3.246403000      0.443720000     15.064121000
C        4.198045000      0.692252000     15.970654000
C        5.531025000      0.961394000     15.546639000
C        6.527506000      1.327523000     16.488699000
C        7.769629000      1.675468000     16.086777000
C        8.044342000      1.864594000     14.697195000
C        9.259232000      2.459858000     14.281133000
C        9.466841000      2.806590000     12.982045000
C        8.445715000      2.608977000     12.035743000
C        7.265466000      1.985829000     12.396483000
C        7.061105000      1.553020000     13.720492000
C        5.833567000      0.912900000     14.172787000
C        4.884651000      0.303088000     13.284635000
C        5.151668000     -0.288539000     12.002691000
C        6.444932000     -0.841371000     11.632053000
H        7.296301000     -1.066868000     13.466331000
H        9.304643000     -2.036748000     12.840647000
H        9.760406000     -2.388329000     10.496986000
H        8.038683000     -1.964007000      8.943383000
H        5.780686000     -1.333585000      8.395468000
H        3.604979000     -0.909262000      9.084780000
H        2.029733000     -0.315211000     10.922946000
H        1.672696000      0.060618000     13.273677000
H        2.290439000      0.327335000     15.253240000
H        3.954366000      0.824398000     16.914659000
H        6.255785000      1.333585000     17.427224000
H        8.447606000      1.891266000     16.702563000
H        9.925491000      2.630800000     14.988120000
H       10.286033000      3.200604000     12.619714000
H        8.559741000      2.909640000     11.135042000
H        6.570317000      1.891266000     11.711236000


M-8a-azonia[6]helicene (from BP86/STO-3G)

N        0.241946000      3.510759000     13.746203000
C       -1.207087000      7.492952000     12.512135000
C       -1.801472000      8.692275000     12.089683000
C       -2.102492000      8.912745000     10.707738000
C       -1.853647000      7.899258000      9.772330000
C       -1.278056000      6.643678000     10.182732000
C       -1.146616000      5.553783000      9.229249000
C       -0.770948000      4.283969000      9.646130000
C       -0.392477000      4.045979000     11.023979000
C       -0.161103000      2.688046000     11.484550000
C        0.042219000      2.428893000     12.821687000
C        0.400500000      3.183323000     15.136378000
C        0.639392000      4.176721000     16.059802000
C        0.949043000      5.527644000     15.625469000
C        1.361398000      6.519481000     16.597330000
C        1.808770000      7.766658000     16.182869000
C        1.981223000      8.066019000     14.770425000
C        2.627560000      9.287588000     14.362758000
C        2.913363000      9.530579000     13.012425000
C        2.578886000      8.546652000     12.028110000
C        1.916409000      7.363991000     12.392255000
C        1.565834000      7.097902000     13.763105000
C        0.907348000      5.851096000     14.211296000
C        0.281492000      4.885356000     13.292158000
C       -0.309154000      5.144896000     11.968134000
C       -0.894790000      6.445456000     11.575101000
H       -1.007504000      7.339193000     13.585554000
H       -2.048406000      9.472285000     12.834293000
H       -2.558542000      9.868716000     10.388465000
H       -2.123797000      8.035037000      8.708340000
H       -1.422274000      5.738729000      8.172836000
H       -0.763274000      3.430969000      8.943112000
H       -0.251900000      1.843110000     10.776492000
H        0.087281000      1.420761000     13.274365000
H        0.295196000      2.107892000     15.372408000
H        0.697253000      3.916258000     17.133249000
H        1.320711000      6.254708000     17.669775000
H        2.110372000      8.530075000     16.926174000
H        2.921715000     10.016221000     15.141242000
H        3.423497000     10.463796000     12.708003000
H        2.853573000      8.716110000     10.969950000
H        1.691114000      6.611596000     11.618453000


$\ce{KO{}^{\mathit{t}}Bu}$ tetramer (from crystal structure)

K       -1.309381000     -1.309381000     -1.309381000
O       -1.313567000      1.313567000     -1.313567000
C       -2.107232000      2.107232000     -2.107232000
C       -3.502008000      2.298114000     -1.478495000
H       -3.842748000      1.465100000     -1.465100000
H       -4.060420000      2.821364000     -2.059512000
H       -3.516240000      2.821364000     -0.619528000
O       -1.313567000     -1.313567000      1.313567000
O        1.313567000     -1.313567000     -1.313567000
K       -1.309381000      1.309381000      1.309381000
K        1.309381000      1.309381000     -1.309381000
C       -1.478495000      3.502008000     -2.298114000
C       -2.298114000      1.478495000     -3.502008000
K        1.309381000     -1.309381000      1.309381000
C       -2.107232000     -2.107232000      2.107232000
C        2.107232000     -2.107232000     -2.107232000
O        1.313567000      1.313567000      1.313567000
H       -1.465100000      3.842748000     -1.465100000
H       -2.059512000      4.060420000     -2.821364000
H       -0.619528000      3.516240000     -2.821364000
H       -1.465100000      1.465100000     -3.842748000
H       -2.821364000      2.059512000     -4.060420000
H       -2.821364000      0.619528000     -3.516240000
C       -1.478495000     -3.502008000      2.298114000
C       -3.502008000     -2.298114000      1.478495000
C       -2.298114000     -1.478495000      3.502008000
C        3.502008000     -1.478495000     -2.298114000
C        1.478495000     -2.298114000     -3.502008000
C        2.298114000     -3.502008000     -1.478495000
C        2.107232000      2.107232000      2.107232000
H       -1.465100000     -3.842748000      1.465100000
H       -2.059512000     -4.060420000      2.821364000
H       -0.619528000     -3.516240000      2.821364000
H       -3.842748000     -1.465100000      1.465100000
H       -4.060420000     -2.821364000      2.059512000
H       -3.516240000     -2.821364000      0.619528000
H       -1.465100000     -1.465100000      3.842748000
H       -2.821364000     -2.059512000      4.060420000
H       -2.821364000     -0.619528000      3.516240000
H        1.465100000     -1.465100000     -3.842748000
H        3.842748000     -1.465100000     -1.465100000
H        4.060420000     -2.059512000     -2.821364000
H        3.516240000     -0.619528000     -2.821364000
H        2.059512000     -2.821364000     -4.060420000
H        0.619528000     -2.821364000     -3.516240000
H        1.465100000     -3.842748000     -1.465100000
H        2.821364000     -4.060420000     -2.059512000
H        2.821364000     -3.516240000     -0.619528000
C        1.478495000      2.298114000      3.502008000
C        3.502008000      1.478495000      2.298114000
C        2.298114000      3.502008000      1.478495000
H        1.465100000      1.465100000      3.842748000
H        2.059512000      2.821364000      4.060420000
H        0.619528000      2.821364000      3.516240000
H        3.842748000      1.465100000      1.465100000
H        4.060420000      2.059512000      2.821364000
H        3.516240000      0.619528000      2.821364000
H        1.465100000      3.842748000      1.465100000
H        2.821364000      4.060420000      2.059512000
H        2.821364000      3.516240000      0.619528000


Grubbs I catalyst

Ru      1.923022    1.782458    4.279841
Cl      3.508375    2.054525    6.061616
P       0.620071    3.495015    5.336792
C       2.967497    2.881791    3.239789
Cl      0.101984    1.197998    2.838894
P       2.855052   -0.401312    3.741075
C       2.954465    3.343954    1.839333
Cl      3.310061    4.678711   -2.473972
C       1.880873    3.257547    0.960743
C       1.973325    3.667349   -0.352875
C       3.185197    4.168660   -0.812833
C       4.252303    4.292067    0.012884
C       4.145603    3.890748    1.341393
C      -0.637087    4.207002    4.175769
C      -1.979932    4.694567    4.692950
C      -2.932151    4.983356    3.538285
C      -2.339331    5.946324    2.517809
C      -0.957803    5.505405    2.056512
C      -0.041546    5.252113    3.235271
C       1.483967    4.856669    6.241316
C       0.518279    5.817396    6.934517
C       1.256971    6.738015    7.899778
C       2.346867    7.495106    7.161401
C       3.302557    6.547168    6.465690
C       2.565538    5.630984    5.497585
C      -0.333586    2.698072    6.719178
C      -1.014762    1.418485    6.241149
C      -1.859827    0.796208    7.358000
C      -1.043744    0.536540    8.601177
C      -0.361483    1.805588    9.075860
C       0.493782    2.427234    7.979254
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