Three ideas come to mind: Knockturn Alley, Percy, and both the part where Dumbledore says help will be given and the part where Dumbledore is talking about Fawkes.
The frustration of the second film is how closely it follows the book but misses some of the je ne sais quoi.

What are your theories about movie 2?
I'll also say that the beauty of the reread is that the first time I read EACH of the books, there was some MAJOR plot twist that seemed TOTALLY random, but on reread either seemed like a minor turn or seemed totally inevitable based on what had come before.
Chamber of Secrets is a good example of this. It's my least favorite book as a stand-alone read. All the red herrings with Hagrid and the spiders, the fact that many people are hurt but not killed through random twists of fate, and Ginny's ultimate involvement didn't make a very satisfying read, but now that we've seen the broader plot there's SO MUCH there for speculation and there's a huge amount of character development that comes back WAY later in the series. This is the book where you learn a lot about Ginny, Riddle, and oddly, Hagrid. (Rowling has said that originally Half Blood Prince and Chamber of Secrets were one book, that she split and rewrote.) I had a special chuckle on the reread with the way she brings Lockhart back into the plot in Order of the Phoenix.
But these plot jerks are why I think a lot of people read the series and are bored or irritated. If I'd only read the series once I would be bored and irritated with it, but right around book 4 the series starts getting really strong plots between the books and the characters start getting more complex.
Snape is a perfect example of this. I was indifferent to him before book 5, and then he suddenly became one of my favorites, especially in the rereads. I'm pretty convinced that he and Dumbledore had a deal, and I'm also fairly certain that Dumbledore doesn't know everything about Snape. There are many years missing between Snape's worst memory, the death of the Potters, and Harry's arrival at Hogwarts that we just don't have information on. After my reread of book 3, it really struck me that the reason Trelawney is at Hogwarts isn't to teach divination, but for her own protection, and it wouldn't surprise me if there was something like that going with Snape (and Hagrid) too.
Draco is a weak person caught in a jam. His parents are evil, and they raised him to be evil, but he still has a choice, and I don't think he's passed the point of no return. Right before Snape arrived, Draco was lowering his wand. I truly suspect that he's never really questioned why he's picked the Death Eater side before book 6. I'd love to be a fly on the wall during the flight of Snape and Draco, especially if Wormtail is a part of that crew. And I'd extra especially like to be that fly if Snape turns out to be good and Draco has really started to think hard about which side he's on. Like I can just see them stopping somewhere for a moment and both just going "Oh shit."
Wormtail is a totally weak and opportunistic person who was also sort of treated badly by James and Sirius, and treated similarly by Snape in book 6. He's weak and opportunistic, but not so weak he doesn't take the opportunities that are given to him. That life debt is still hanging out there. Sirius and Lupin would have killed him, but Harry said he didn't think his dad would have wanted them to become murderers, so Harry made them spare Wormtail. He's also been listening at doors...
Rowling's got such a complicated cast with all of them having strong opinions of one another.... I think the thing that has really sucked about the movies is how they focus more on the physical scenes, but the real joy of the books is in the scenes where the people are just talking and interacting with one another.
What scenes are your particular favorites, just out of curiosity?
