Continuity mistake: After the scene where Jacob rescues Bella from the ocean, when they're driving home it's not dark outside as they're pulling up into Charlie's driveway. But once Jacob starts talking about Sam and Emily, it's darker outside. Even after they get to the door.
Continuity mistake: In the scene where Bella jumps off the cliff, Bella's eyes are brown before jumping but are blue/green when she surfaces in the water and then back to brown in the underwater and shore scenes.
Revealing mistake: When Sam comes into the house and kisses his fiance, you can see the ripples in the edges of the plastic film used to put the tattoo on his arm.
Continuity mistake: In the scene where Jacob is talking to Bella on the beach about Victoria, his shirt starts off as a dark gray colour, then it changes to a brown colour. It does this a few times during the scene.
Continuity mistake: In the last scene when Jacob confronts Edward and Bella. Edward's hair is it's usual poofed up, uncombed look but after Bella separates Jacob and Edward and Jacob runs off, when the camera is back on Edward, his hair is flat and neatly combed, then within a few seconds it's back to its uncombed look.
Revealing mistake: When Bella and Edward return from Italy, Edward 'disappears' when Charlie enters the room. You can see behind the door when he is in the room that there is nowhere/not enough space for Edward to hide, but when Charlie leaves the room, as the door shuts, Edward steps out from behind it.
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.
Deliberate mistake: In the scene where we see Bella in her room looking out the window, the months are passing, but she is always wearing the same clothes.