First off let me say that I loved the movie and I thought it was great! Now with that said...
After reading the books at least 3 times through and rereading several parts uncountable times I was looking forward to seeing a few things on screen which unfortunately for me were not in the film. Here are just a few of them (I admit most of them deal with Narsil/Anduril) :
1. In the Hobbits' room in Bree when Strider identifies himself as Aragorn son of Arathorn and then he takes out Narsil and the hobbits see that it isn't a complete sword
2. The Council of Elrond (what was on screen was good but...): no Bilbo and his speech, no Boromir's dream (in detail nor mention of his brother Faramir) and Aragorn saying "Here is the Sword that was Broken" and thus identifing that he is Isildur's Heir, Gloin's speech how an emissary of Sauron went to Erebor offering the 4 surviving Dwarven Rings to King Dain II Ironfoot
3. No re-forging of Narsil into Anduril, I guess my biggest problem with leaving the sword out was that Anduril was one of the few Magic Items that has any prominance in the books that Men have(Gandalf's staff, Glamdring, Sting, Palantir, and of course the Rings of Power- only the Minas Tirith Palantir is in the hands of Men), Aragorn uses Anduril throughout the books and it is specificly stated that it is the ONLY weapon he takes with him when he leaves Rivendell (though Tolkien does say that Boromir's Sword is one of less lineage than Aragorn's but we never see any effects like Anduril's flame), that's my biggest problem with leaving out Anduril. In what many people feel that Middle Earth is a low magic world Narsil/Anduril is important to the story (IMO) and it is a connecting point with Aragorn and the First Kings of Arnor and Gondor.
4. Only references to Gondor and none about Arnor, there were two kingdoms of men in the West. Elendil founded Arnor (Royal Land) and his sons- Isildur and Anarion founded Gondor (Stone Land) but I do understand that PJ would leave out a kingdom that doesn't exist anymore, but the mention of Aragorn living in exile was way off IMO. Yes I know that is nitpicking but this thread is about what we didn't like about the film.
5. Where was Galadriel's Ring Nenya?
Well, with that said I still think it was a GREAT film. I've seen it twice and I might go see it again and I will definitely buy the DVD and will go see the next two films.