The first 25 minutes or so is new material not found in the book, mainly focused on Barbara Gordon. I found this to be an improvement as the comic book more or less brings Barbara on in order to
her as part of a scheme whose main target is Commissioner Gordon. There has been some controversy about
but again, to me, that is an improvement as it is a natural development.
the introduction of a sexual relationship between Barbara and Bruce
The remainder of the movie represents the book pretty faithfully except that the Joker's backstory is presented in smaller chunks. It is well done.
Basically since TKJ came out nearly thirty years ago, there has been discussion about the last page. The joker has told a somewhat grim joke and is laughing away in the rain, and Batman starts chuckling as well. Batman has his arms high up on the Joker's body. The police arrive with sirens blaring. From one frame to another the laughter stops, and the final frame is the puddle of rain in the dark.
Some people have said that this implied Batman choked or snapped the neck of or otherwise killed the Joker. This would be a reasonable thing to happen, given the prior events of the day. Moore's notes do not indicate this happened but I don't know whether he intended to imply it. The artwork makes it look more like he is reaching for the Joker's shoulder rather than neck.
On the other hand, Bruce to just be having a regular laugh with the Joker on this day makes him seem callous. If he is just sharing a laugh, the reason for the sudden stop is that he does not want the police to see him laughing with the Joker.
In my head, that last page represents the fact that the Joker is a bit correct: Batman is somewhat insane too, driven that way by a tragedy that the Joker can only guess at. He has a dark, unwell sense of humour, and a well-balanced person would probably not be able to have a chuckle with someone who had done the Joker's deeds that day. The nature of the laughter in the movie is compatible with this idea. Bruce sounds a bit manic.
We are used to Moore having contempt and disdain for the films based on his comic books, but in the case of The Killing Joke, he has contempt and disdain for the comic book itself. His comments on TKJ hint that he did not enjoy the confines of these characters that had been defined by others, and that he considered unrelated to the real world.