First, I'm not sure that there are very many uses of Facebook in education outside of Facebook's original purpose, which is to socially connect and network people through the Internet. In this way, I think the educational advantages lie mostly in Facebook's size, availability, and propensity for quick connections.
As a teacher in a private school, I decided (after a few years) to go ahead and accept student friend requests, and to be honest, it has had far more advantages than disadvantages. First, my personal connection with students grew much more quickly. They felt immediately more connected to me, and in turn, opened up more in my classroom. Their greater interest in me translated into a greater interest in my class. Also, many of my students used Facebook to contact me with homework questions. I believe our high school and college students (as well as many adults) have largely moved away from the generation of email as a quick mode of contact, and Facebook seems to be a "safe" and easy alternative. I rarely had students who emailed homework questions, but the minute they could catch me on Facebook, personal contact increased exponentially.
Finally, now that many of my students have graduated, I've kept in contact with many of them in college. This has led to several seeking advice with college papers, internship connections, and sometimes reference letters. I think Facebook has benefited the students more than me, and this, simply because it is something they are not afraid to use. I remember being terrified of attending professor "office hours" in college, a piece of advice I now wish I'd heeded with more regularity. I think Facebook takes away much of the intimidation students have for communicating with their teachers, and that, to me, is definitely an educational advantage.
You might be interested in some other open discussions concerning Facebook by following the links below.