What's the correct graphical interpretation of a series of MFCC vectors?
The way MFCC's are always used is by feeding them into the classifier. This can be done on a frame-by-frame basis (12x1 vector), or by concatenating (12xN) - same as a spectrogram. 

Thus for DTW, you must perform the classification by calculating the distance between 12D vectors. It's a Dynamic Time Warping, so the difference must be calculated between frames in time domain, not between samples in a "single feature domain".

Here is a graphical representation of that:





Just an addendum on MFCC plotting. There is no point in looking at the line plot of all MFCC vectors stacked together (first image), and it's not really useful to look at the time evolution of all MFCC's (second image). No concept of right graphical representation exists for MFCC's unless you want to achieve something specific.

Firstly, a distribution (histogram) of each MFCC can be plotted to see what are the typical values, etc. Especially if you have a GMM model trained for a signal, you could plot the distribution of test sample and overlay with a PDF of GMM in that dimension.

The second approach would be to plot the MFCC's similarly to a spectrogram (as shown in the picture above). One might want to use it for "nice representation" or seeing the overall trends and patterns. But it's almost impossible to tell what kind signal is hiding behind such representation.

For example, here is an MFCC plot of a very simple signal. What signal is that? If you are ready then please hover the yellow space.




   Exponential sine sweep!
 


Was it easy to tell? Definitely, by looking at the spectrogram it was immediately obvious. Maybe there are few people who guessed since they played with such examples before. Now something more complicated:



Ready?


   Birds chirping - you can listen here
 


I hardly think so that this MFCC representation is of any use, except filling the space. Now few people might guess the signal based on a spectrogram, but it's impossible to do so by looking at MFCC's. 

So if someone is telling you that he can tell what is happening with the signal based on "de-correlated cosine fits of log energies within triangular filter banks in frequency domain", then he is either a liar (with a prior of $99.9\%$) or a computer.  Very rarely there are occasions when looking at raw MFCC values is useful - like debugging and sanity checking (are coefficients constant for stationary signal).