First of all, I'll say we both enjoyed the film, as we had enjoyed the books. The film followed the first book pretty closely, about as well as one can expect when a book is made into a movie. If there were major deviations from the book, we didn't catch them, but it has been several years now since we read it. The movie was beautiful to look at, and the characters were nicely realized. And, hey, it has armored bears!
They did attempt to tone down the books' anti-Christian themes somewhat, dropping references to "The Church" and "priests" and speaking only of "The Magisterium." The net effect is to make it more ecumenically anti-religious. Chances are that showing this in many Muslim countries would result in a mob burning down the theater, and possible prosecution/lynching of those involved in showing it. Keep that difference in mind, if you find yourself about to denounce Christian groups for calling for a boycott of the film.
This is based on the first book of three, and clearly they are planning to make the trilogy (next: The Subtle Knife), if the response justifies the cost. The movie ends right before the end of the first book, as Lyra and Roger are on the way to meet her father. It appears as if that encounter will also match the story in the book.
This is absolutely not a movie for small children, religious or not. It's rated PG-13, and appropriately so.
SPOILER ALERT: (Don't read on, if you want to avoid story spoilers)
Roger's impending death at the hand of Lyra's father (at the start of the next movie) is just one reason this is not for small children. The religious authorities are kidnapping poor children. They are experimenting on severing children's souls ("their demons" in the story) from their bodies to produce more docile adults. The process and results are scary and sad. There's quite a lot of violence, although not overly graphic by today's standards.
It's not until the next book that we encounter the evil angels and not until the third book that Lyra and friend actually kill God. In the end, God is revealed to be a doddering old fool, virtually unaware of anything going on around him. His power has been usurped by another angel who rules in his name. The actual killing of God is essentially portrayed as a mercy killing, putting him out of his misery.
So if you read and liked the books, chances are you'll enjoy the movie, too. On the other hand, if your religious faith is an important part of your life, you may very well find the whole story more than a little insulting. The claim that the story isn't really about religion, but just about the need to keep religion and politics separate doesn't ring true for me. That theme is there, but there's really no positive religious image ( e.g. non-political) that would draw that distinction.
UPDATE: Here's an excellent article about the books and the movie from a Christian perspective (H/T Mark F).