There’s a fan site called Bridge to the Stars, which highlights two passages which are significantly different in The Amber Spyglass:
Are there any differences between different editions of the books?
Some later editions of the trilogy, such as the Lantern Slides editions and the Tenth Anniversary editions, include special extras
created by Philip Pullman – where we can, we’ve uploaded these in our
Extras galleries.
There are also some differences between the UK and US editions of the books. The most significant change is perhaps the
omission/amendment of a couple of passages in the US edition of the
books. We’ve detailed these below.
The Amber Spyglass: Chapter 33, Marzipan – UK EDITION
As Mary said that, Lyra felt something strange happen to her body. She felt a stirring at the roots of her hair: she found herself
breathing faster. She had never been on a roller-coaster, or anything
like one, but if she had, she would have recognized the sensations in
her breast: they were exciting and frightening at the same time, and
she had not the slightest idea why. The sensation continued, and
deepened, and changed, as more parts of her body found themselves
affected too. She felt as if she had been handed the key to a great
house she hadn't known was there, a house that was somehow inside her,
and as she turned the key, deep in the darkness of the building she
felt other doors opening too, and lights coming on. She sat trembling,
hugging her knees, hardly daring to breathe...
The Amber Spyglass: Chapter 33, Marzipan – US EDITION
As Mary said that, Lyra felt something strange happen to her body. She felt as if she had been handed the key to a great house she
hadn’t known was there. A house that was somehow inside her, and as
she turned the key, she felt other doors opening deep in the darkness,
and lights coming on. She sat trembling as Mary went on...
The Amber Spyglass: Chapter 35, Over The Hills and Far Away – UK EDITION
...Father Gomez found himself praising God for his mission, because it was clearer than ever that the boy and the girl were
walking into mortal sin.
And there it was: the dark-blonde movement that was the girl's hair. He moved a little closer, and took out the rifle. There was a
telescopic sight: low-powered, but beautifully made, so that looking
through it was to feel your vision clarified as well as enlarged. Yes,
there she was, and she paused and looked back so that he saw the
expression on her face, and he could not understand how anyone so
steeped in evil could look so radiant with hope and happiness.
His bewilderment at that made him hesitate, and then the moment was gone, and both children had walked in among the trees and
out of sight. Well, they wouldn't go far. He followed them down the
stream, moving at a crouch, holding the rifle in one hand, balancing
with the other.
He was so close to success...
The Amber Spyglass: Chapter 35, Over The Hills and Far Away – US EDITION
...Father Gomez found himself praising God for his mission, because it was clearer than ever that the boy and the girl were
walking into mortal sin.
He watched them go in among the trees. They hadn't looked back once since coming over the top of the ridge, but he still kept low,
moving down the stream at a crouch, holding the rifle in one hand,
balancing with the other.
He was so close to success...
The reason for these changes is unclear, but it is thought that the first is due to the passage being interpreted as of a sexual
nature.
There’s a forum thread on the site where fans have been discussing the differences between the UK and US editions.
It’s clear that there are changes in all three books, but nobody has identified anything as notable as the above. The other differences sound fairly minor: changes in vocabulary (e.g. “trainers” vs “sneakers”).
Note: anecdotal evidence from that forum thread is that North America all got the same editions – although the text above distinguishes UK/US, these changes were also present in Canadian editions.