Qualified to perform the work you hired him to perform?
In any event...not paying the guy because you believe he "committed a few crimes" and crossed the border illegally is pretty shady on your end and looks as though you are trying to screw him over because he is powerless to do anything about it.
Not paying him because he did a really crappy job is a little different...but you need to understand why he did such a crappy job. Does he think he did a poor job? Did you tell him that you had a problem with his work?