One problem with Facebook is the overwhelming flood of applications available for it. While this seems like it'd be a good thing, the problem is that whenever a user installs one of these on his or her profile page, the application usually prompts them to automatically forward an installation request to every single one of their friends. As you might imagine, this kind of thing can quickly get out of hand.
Another issue is the continuing erosion of the barriers to Facebook entry. Originally, the site was limited only to Harvard students, but it was later opened to all Ivy Leaguers, and then to all college students. Now, it seems like anyone with a pulse (and even some without) can get a Facebook account. I hope it never happens, but I can imagine people eventually wading through armfuls of Facebook spam.