Right before Jacob jumps through Bella's window you can clearly see that her desk is pushed up against the same window but when he jumps through it, the desk is moved to a completely different spot in the room. Once he jumps out again the desk is moved back to its original location in the next scene.
In the scene when Bella first joins her friends at the table in the school cafeteria after her long depression, as she is talking to Mike, if you look at her hair by her left ear, you can see a bobby pin that may have fallen out of her hair piece or is just not hidden well. When the scenes changes to Mike and then back to Bella the bobby pin is gone.
When James bit Bella in Twilight, his upper set of teeth marks are in the center of her wrist, with the lower set being on the side of her wrist. When you see Bella's scars in her room with Jacob, the entire set of teeth marks have been shifted markedly to the right.
When Bella is in the kitchen telling Charlie and Harry Clearwater about seeing the huge wolves in the woods, there is clearly no phone on the wall between the cupboards and the doorway - however towards the end of the film, Jacob answers Edward's call using a phone on the wall, that wasn't there in the earlier scene.
When Bella ditches Jessica to ride with the guy on the motorcycle, she disappears between shots and changes in camera angles. At the beginning when they are driving away you see her on the back of the motorcycle, but in the next shot she is gone for a split second and then back again in another shot before she sees the hallucination of Edward in the road ahead.
When Mike and Jacob go to the cinema with Bella, Mike is wearing a jacket, but when he leaves his seat in a hurry to go to the men's room, he doesn't appear to have his jacket with him, although he is wearing it again when he rejoins Jacob and Bella in the foyer.
When Bella arrives at Jacob's house in La Push with the two motorbikes, she parks her truck next to a silver truck, but when the shot widens out, the silver truck in now parked some way in front of her red Chevy.
When Bella is trying to reach Jacob after his abrupt departure from the movie theater, she is in her living room doing her homework while her father is watching an Arizona Wildcats college football game on TV. Football season would have been over by this time, which should have been March or April (according to the fact that Bella's last visible email to Alice was on February 13, her sent email folder is organized by date and the last emails she's sent are at the bottom, as evidenced by the fact we see February 11, yesterday and today at the bottom) and she had spent at least a month or so working on the bikes with Jacob).
Laurent doesn't glow like the vampires do, though he is outside. However, it's not so much sunny as overcast. We see Edward and the other Cullens outside many times during the day when it's light but overcast, and they never sparkle.
When Bella and Jacob are driving to ride the bikes, as they are being filmed in the truck's cabin, the shadows from the road trees are passing like they were driving backwards instead of driving forward.
After Bella's birthday, which is when she receives a digital camera, she takes her camera to school and takes a picture of her friends. The image in the view-finder does not match with the scene being photographed. In the scene, there are two people walking behind her group of friends that don't appear in the view finder.
The goof items below may give away important plot points.
In the scene after Bella finds out from Laurent that Victoria is after her, she is sleeping in her bed. The dream catcher is hanging to the side of the round circle on the headboard. After Jacob climbs into Bella's room - he focuses on the dream catcher. The straps are now encircling the headboard.
In the first clips, when Jane is leading Edward, Bella and Alice to the Volturi, her hair is twisted at either side into a bun. But as she enters the Volturi chamber, her hair is smoothed on both sides into a bun.
In the scene immediately following Bella, Edward and Alice's return from Volterra, Bella wakes up in her bed screaming. She is wearing a tank top, however, there is no scar on the upper right portion of her arm from when Dr. Cullen had to stitch her up after Jasper's attack on her birthday. As it had only been a few months since the incident Bella should have been sporting a scar.
Bella is said to be immune to vampires' special abilities as highlighted when facing the Volturi, however, Jasper is able to control her mood in regards to her birthday party. In fact, her immunity is to powers that affect the mind, whereas Jasper's powers affect the hormones that control emotions.