Enzymes extracted from diferent tissue, may have diferent $K_m$ values under the same conditions?
You would not expect the same enzyme from different tissues to have different Km values if the enzymes are truly identical. 

In addition, you would not expect the Km value to change during purification: the Michaelis constant for the purified enzyme should be the same as that determined with a crude sample.  If this is not true, it might mean that the enzyme has become modified during purification, perhaps by proteolysis (not something you want your examiner to point out or suggest!). 

One advantage of the Michaelis constant is that it is independent of enzyme concentration (and so does not depend on the degree of purity).

Having said that, I think it would not be considered too unusual for enzymes isolated from different tissues to have different Km values.  

Possible reasons are:


The assay conditions are not really the same. pH, ionic strength, temperature and buffer composition may all affect  Km.  The Michaelis constant determined at pH 7 in 100mM phosphate at 37oC may be very different from that determined in 50mM Tris pH 7 and 25oC
Post-translation modification may be important.  The enzyme from one tissue may be phosphorylated, for example. One laboratory may have isolated the modified from, whereas another laboratory may routinely include phosphatase inhibitors.
Proteases present in the crude tissue preparation may have modified the enzyme.


In the case of succinate dehydrogenase, there are two other important considerations.


Succinate dehydrogenase is a membrane-bound enzyme (containing a covalently bound flavin) and the method of extraction will be all-important, and a key area to examine is whether extraction conditions may account for the difference in Km.
Finally, and this one is important I think.  SDH is a two-substrate enzyme and the Km for substrate A will depend on the concentration of substrate B ! To determine the 'true' Michaelis constant for a two-substrate enzyme (assuming no substrate inhibition), we must extrapolate to 'infinite' concentrations of the co-substrate. Otherwise we are dealing with apparent Km values.


I'll bet the last point is important. Is the problem that at least some of the reported Kms are apparent values, ie the concentration of co-substrate is different under the different experimental conditions?