Why not? Where do I start.

Well, let's see: 'Your honor, I married this woman because I thought she was filthy rich. She wasn't, but I sure am. I'd like a anullment.' doesn't sound like Clooney's charachter does it? Your nitpick states he's never heard of a annullment. Where in the movie does it state he's never heard of an annullment? This falls under charachter stupidity, or 'needed for plot'. Refute please.

Whoa, hold on a minute

Most quick Vegas weddings could be annulled within a few days regardless of the reason. In this particular case, Miles Massey was the victim of a pretty malicious fraud. Besides, I think you should watch the movie again, because he didn't marry her for her money -- rather, she married him for his money, and staged an entire fake marriage to do it. Because of her dishonesty, any judge would have annulled the marriage so that she couldn't succeed in essentially robbing an unsuspecting dupe of half his fortune. Not seeking an annullment goes well beyond the realm of character stupidity, since as a lawyer (the TOP divorce lawyer in town, we're told), that would be his first action. His first step would not be to seek an asthmatic hitman.