This is not a movie for Tolkien purists, first of all. Events have been accelerated to fit them into three hours. Lobelia Sackville-Baggins has disappeared but for someone pounding on the door. The lovely scene with the presents from Bilbo and the notes as he distributes his household to friends and family is entirely missing as well. Gandalf does not cover for Bilbo's ass as he slips the ring on and disappears. But the old gaffer who yells "Proudfeet!" is still there, much to my delight.
Merry and Peregrine are still jolly rogues.
Perhaps the largest bust of continuity is that Frodo sets out directly following Bilbo's disappearance, almost -- he is barely given time to realize that it's he who's got Bag End now before Gandalf sends him scurrying off willy-nilly to get the hell out of town because the Black Riders are damnnear at the door.
The movie follows Gandalf as well as Frodo -- the things that Gandalf only summarizes in the books are seen, and we get to see the lovely mage-battle between Gandalf and Sauraman, with some lovely phrasings of Gandalf's. The line "Do not meddle in the affairs of wizards, for they are subtle and quick to anger," is missing.
Arwen is the elf who rescues poor Frodo with the splinter in his shoulder, and does the whole Heroic Knight bit on a lovely pale grey horse, with ringwraiths in hot pursuit.
Merry and Perrin (so sue me, I know I'm screwing with his name, but I've been reading Wheel of Time too much, and LotR too little) play with Gandalf's fireworks and get scorched some. That's amusing.
"Fool of a Took!" makes it in.
I can't read the runes that Tolkien uses; they look almost but not quite like the Elder Futhark. Same shapes, but different language.
Bill Ferny is absent; Bill the pony gets picked up without comment and is only briefly said goodbye to. Barliman Butterburr is all but absent as well; he is never shown by name; even his name has come off the sign of the Prancing Pony.
Sam Gamgee is portrayed far differently than in the book. In the book, he comes off to me as shrewd, cunning, clever, and fiercely loyal, as well as creative. In the movie, he's got a far less distinctive personality, and is chiefly portrayed as loyal. We don't get to see his wits in action, but we do get to see him nearly drown.
The special effects when Frodo puts on the ring are astounding and wonderful and I love them to bits. You really do get the idea of being half in and half out of another world.
Not enough of the elven/dwarven race conflict is portrayed; the bit with the blindfolds is entirely left out. Darkside and I elbowed each other on that one.
The "shortcut to mushrooms" is changed almost all out of recognition; that's where Sam and Frodo meet up with Merry and Perrin, and they get chased by the farmer, and get chased almost directly into ... well... you can watch it for yourself... it's scary.
Strider is just as scruffy as advertised. I am told that he cleans up well.
Tom Bombadil and Goldberry and Old Man Willow were cut. So was the several months with Arwen's family of elves, and so was the dinner party when Frodo finally came out of his coma.
There's by far not enough singing in the movie. You can't have hobbits without song, and there is a little, but not enough. The tone of the movie is far more frantic than the book -- the book starts out far slower. Frodo gets shoved head over heels into adventure, rather than choosing to leave of his own accord.
There is a cute moment with Gandalf, very reminiscent of Luke Skywalker in Yoda's hut.
Aragorn's sword is not covered deeply enough. We do see it lying shattered, but we never see it made whole.
We do get to see Bilbo gift Frodo with the armor, and Frodo's near-death in the Mines of Moria is well-done indeed.
The opening of the gates ("Speak friend and enter") is not quite to specs, but damn close except where the tentacle-monster begins to emerge from the lake. Gandalf's double-take could have been better-done, but they were pressed for time.
All in all, most of the changes were made as edits for length, and the overall effect of the story, except for the slow beginning, remains.
I highly recommend this movie, more than once.