Requiring a Facebook account in order to register for an application is a really bad idea. I’ll concede that there is a very large segment of people that don’t mind, but for every person that doesn’t mind, there are two power users that do.
First, Facebook is a privacy nightmare; they have the potential to track your every move across the Internet and they will if given the chance. This scares the hell out of me. I mean who wants everything thing they do on the Internet broadcast for everyone?
Second, you’ve now created a Facebook plugin. You are so tightly coupled to Facebook that you will have trouble decoupling that relationship and having your own app. My guess is that you will have to start over.
I’m good with Facebook integration, but give me a choice. Let me decide if I want my information broadcast to Facebook. Apps should have their own identity and tie into other application as options, not requirements.