I love the books and have read them all, including the most recently published. The BBC adaptation has many good points, including the portrayal of people's daemons, but I must take issue with a couple of things.
As I remember, Lyra didn't know that Lord Asrial was her father until much later in the book, and there was no interaction between different worlds until the second book in the series, The Subtle Knife.
Be interesting to see what other spoilers they introduce.
If you haven't yet read the books, but are inspired to do so by this adaptation, record the remaining episodes and read the books (all three in the trilogy) and then watch the remaining episodes!