No doubt it would be dirty, but I'm not sure it would be unconstitutional. I haven't really read up that much on it though, so who knows what would happen. It would be comical to watch though, because you know he would take that all the way to the supreme court if someone tried to stop him.So it's a bit of a debate on whether he would be eligible to run again. The Constitution doesn't implicitly state he can't, but Hamilton's discussion on impeachment suggests that he should not be able to run again.
Something about taking the Oath of office when you've already been convicted of breaking that oath seems dirty to me.