OK. TW, this is No. 7 here. I still think I'm correct, but I'll be a little less sarcastic in this post here.
The only possible problem that there could be with trying to get involved with this guy is if there complications because, say, he's teaching your class, or because he's, for example, the brother of the guy teaching it. It's possible that, wherever it is that you happen to live, it would be questionable even just to get involved with a faculty member of the university or college, regardless of how distant their position/department is from the teacher/department with which you are associated.
However. You said yourself that he's not teaching the class. Chances are he's not related to the teacher, either. And even IF your university is that freaking paranoid about people working the system by having friends in high places, the chances that it would cause any trouble for you are probably minimal. That's IF your university is that paranoid.
I only know what you've shared with us in this thread, but it seems to me like you're just intimidated by both the fact that he's probably more capable than you (which is simply because he's taken more classes than you, you realize) and the fact that his Ph.D. automatically marks him as academically superior.
These are not things that should get in the way of romance.
I guarantee you that if this man is going to take a liking to you, he's not going to care if you don't also have a Ph.D. If he does, then he's a douche and you shouldn't be with him anyway. It may be true that he possesses a higher status than you in the world of academics, but I highly doubt that he would let his Ph.D. play much of a role (if any) in determining who he gets romantically involved with.
Besides, if you don't try, then you'll never know. It's not like the man is married or already has a girlfriend. It's not like you're cheating on anybody, since you don't have one, either. You've got nothing to lose, because even if he does reject you, and even if it IS for some retarded reason like "You don't have a Ph.D. like I do," there will be absolutely no lasting negative effect on your life. It's not like it'll prevent you from continuing your education or from getting a good grade in your class or anything.
And that is why, in my humble opinion, you should hit on the man.