Continuity mistake: When Bella is in the parking lot at school in the beginning, Edward walks toward her. Bella's hair is neatly pulled off to the side. When he leans in for the kiss it is suddenly stuck to her forehead, and when Edward tells her Jacob wants her, it's suddenly back to normal.
Continuity mistake: When Bella goes to the Cullens' house for her birthday party, Alice takes the new camera that Charlie got Bella and takes a picture of Bella and Edward. But when Bella prints out the picture and puts it in her scrapbook, it looks nothing like the picture Alice took. Given we see the entirety of her visit from start to finish, there was no other opportunity for a different photo to be taken.
Continuity mistake: During the paper cut scene, when Bella is thrown against the table, there are 5 vases of flowers and 3 sets of candles. After she hits the table she lands against one of the vases and knocks the 2nd one to the floor, but the next shot shows only one vase left upright.
Continuity mistake: In the scene where Carlisle is treating Bella's wound there is a shot of the bowl where he is putting the glass from the wound. You see that there is one piece of gauze. He then starts stitching up the wound and when he lights the contents of the bowl, you see lots more gauze that he hasn't used in there.