How does it read? Pick a module, remove all its commentary. Read the code, possibly aloud. Can you follow it? Do the method names make sense? Is the layout consistent? Good code expresses the programmer's intent in clear, readable code that doesn't depend on comments. Comments, where they exist should only have to explain the why of the code. The code itself should tell you how.

Is there a fully automated test suite? The lack of one doesn't necessarily mean the system is crap, but it's not a good sign.

Try and implement a new feature (or ask another programmer to do so). How hard was it? Can it be done? Can it be tested?

Will the software engineering company stand behind their code? Will they give you a warranty (unlikely) it (or offer a reasonably priced support contract).