In the first book, Hagrid says that James and Lily Potter were Head Boy and Girl during their seventh year, but then in Order of the Phoenix Sirius says that he and James weren't made prefects in their fifth year. So how the heck did James get to be Head Boy?
As far as I can recall, it's never explicitly stated in the books that being a prefect is a prerequistite for being Head Boy or Girl (though it is implied), so I guess that might explain it, although it does beg the question of why Dumbledore suddenly decided that James should be entrusted with this responsibility. And it really bothers me because I'm still mystified as to how Lily and James got together, and the getting to know one another through Head Boy and Girl duties makes sense to me(although I hope it wasn't how it always is in fan fiction where they share dormitory, because ew!), but then it doesn't make sense how James got to be Head Boy in the first place. Darn you, Jo Rowling!!!!!!!!
One of these days I will go back and talk about all my many thoughts and reactions to the end of the Harry Potter series. I really want to; it's just that there's a lot of them, so it's going to take a lot of time to write them all out. And I have other stuff going on.