I would have liked to hear more about what was going on with the other people as well, not just with those at Hogwarts, but with the Order and Ministry and all those too. I guess that would have made for a really long book though...I just thought that some of the parts from Ron, Hermione, and Harry's months wandering could have been cut down a bit too add more for other things. Then again, the books have generally been told almost from Harry's point of view, so it wouldn't have really fit with the rest of the books...
I actually thought that the stuff about Dumbledore's family was pretty important to the story. Ever since the Order of the Phoenix, we've been given hints about Dumbledore's weaknesses. We've also known from the first book that Dumbledore has understood Voldemort in ways every other witch or wizard has been unable...From what we learned about Dumbledore's past, he could have become like Voldemort except for that very important magic that Dumbledore has always told Harry about...Love...Dumbledore's love for his family seems to be what kept him from going down that path.
I thought about the possibility of Snape being Harry's father for about 1 second, but Harry has always been described as the splitting image of James, except for Lily's eyes.
I would like to know more about what happened in the wake of Voldemort's death.
How did the Weasleys cope with Fred's death. I couldn't believe that one, I kept waiting for Fred to get up.
How had the experience changed the Malfoys, or did it change them at all?
How is everyone getting along with Percy since he seemed to come back?
Harry and Ginny had named one of their sons "Albus Severus." How were they able to forgive Snape enough to name one of their children after him, but seem to still have a strained relationship with Percy?
Did Professor McGonnogall become the next Headmistress of Hogwarts? The office had opened for her as the "rightful headmaster" at the end of the Half-Blood Prince, but then Snape was able to get it during his reign. Why did it let him in? Was he the rightful headmaster just because of his service to Dumbledore?