Inspired little character and staging details
I really like this one the most, think it's the best HP-film by far. It looks excellent, the story is well told and well paced. It seems to have more composure than so many of the other films, it gives room to the characters.
Also: little inspired touches that really make the magic world come alive, like the cleaning lady in the hotel that opens a door and then is screamed at by some creature we never see, the over-submissive hunchback servant, the candles that are spines, with numbered vertebrae!
It's these little touches that really make a story come to life. Maybe you don't even notice them consciously, but your brain does.
Also the mise-en-scene in this film is often inspired. Little things like Harry playing with the candle when Lupin is teaching him the patronus spell, Hagrid standing with his trousers stripped up and throwing pebbels in the water, like a sad kid, when he tells that Buckbeak has to die.
In other movies this information might have been exchanged between two talking heads in a generic room, but by doing something just a little more creative with little scenes like that, you really make it work.