To start with my one disappointment: there were a few parts which seemed really slow to me: council meetings which didn't illustrate much; political comments from minor figures. I wanted to get to the action!
Both this book and The subtle knife move between characters quite a lot; you see Lyra, and then just when it gets really exciting it changes to see what Will is doing, and then it skips to Dr Mary "Tempter" Malone in a world of diamond-framed animals on seedpod wheels.
OK, I thought the seedpod-wheeled animals were awesome. I want to see them in the movie. But still. Very effective technique on the part of Mr Pullman; but damn, I could not read that book fast enough.
Couple of quibbles again: I found that Dr Malone acted younger than she was: some of her dialogue didn't quite "mesh" for me. But it is a young adult book, so the language probably worked better for the target audience.
Also, a couple of loose ends weren't really explained for me. We're introduced to the soul-eating Spectres in Book Two; but for some reason, two characters in Book Three wander around happily without ever being affected by the Spectres. Why? We're never told.
This trilogy really reminded me of what some people said when I told them my theory about the Christian God. Our theories are virtually identical, which irritates me. I'd started to write a story incorporating my theory (similar to how Pullman did it, only from Lucifer's point of view instead of from humans' point of view) and now it'll all seem like plagiarism. So there goes that brilliant idea!
Maybe it just goes to show that great minds think alike.