Well, I think I he has a girlfriend then he is off limits, unless he or she or they together decide to call it quits.

You mention her negative traits, there is usually two sides to every story. So I would try not to bash her too much. Its easy to do as an outsider looking in. But it can be a whole other story between the two in the relationship. An example might be that she could possibly feel that she has a boyfriend who flirts with other girls, lends them his hat and what not. Maybe she isn't just the " jealous type", possibly she has a reason to be jealous?

Honestly I'd try to stay out of it till they decide that it's over.