What is the main limitation of DES? I know this question seems too general, not specific. Our professor asked this question today, and I have no idea how to answer it.

Maybe it's the key size, maybe another thing? Any idea?
According to Introduction to Modern Cryptography by Katz and Lindell, in the section titled Security of DES on page 218 in the second edition.


  After almost 30 years of intensive study, the best known practical attack on DES is still an exhaustive search through its key space... Unfortunately, the 56-bit key length of DES is short enough that an exhaustive search through all $2^{56}$ possible keys is now feasible.


They go on to say (a few paragraphs down):


  The insecurity of DES has nothing to do with its design per se, but rather is due to its short key length... Since DES itself seems not to have significant structural weaknesses, it makes sense to use DES as a building block for constructing block ciphers with longer keys.


So I would say that yes, the main limitation of DES is the key size.

That book goes on to state the secondary cause for concern as the short block length of 64-bits.