IMDB has added a cool list of goofs that happened in New Moon. Most of them aren't as noticeable as Twilight, where you saw boom mics in reflections of windows and etc..
Continuity: While Bella and Edward are embracing each other right after they met up in Volterra and are interrupted, Edward's body is not completely "whited-out", only his face is. This is going on the entire time he is speaking to someone in the Volturi. His face is extremely pale, but his neck and abdomen are the color of a human being.
Continuity: After fighting with the Volturi, Edward's robe changes between being tied closed and completely open.
Revealing mistakes: In the scene in Bella's bedroom after Edward's return, the camera shakes as if someone has bumped into it.
Continuity: 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.
Continuity: During the scene where Charlie is telling Bella she is going back to Jacksonville because of her depression, the part in Bella's hair changes slightly between shots.
Continuity: Bella's hair color changes frequently. In some shots it is clearly black, whilst in others it is Bella's normal brown.
Revealing mistakes: When Bella is talking to Jake in the rain, only the front of her jacket is wet.
Revealing mistakes: When Jacob tries to wipe the blood from Bella's head with his shirt, the blood doesn't smear or run at all, as if it was painted on or drawn on with a marker.
Continuity: Bella and Alice's relative height changes frequently throughout the movie. (Bella is supposed to be taller than Alice, but Ashley Greene is taller than Kristen Stewart.)
Revealing mistakes: In Port Angeles, Bella is riding on the back of a motorcycle. When there is an overhead view of the bike speeding down the street, it is obvious there is only a driver and no back passenger.
Continuity: 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.
Crew or equipment visible: During the scene after Edward leaves when Bella is sitting in the chair in front of the window. As the camera spins around Bella the first time, you can see someone in the mirror. I remember seeing someone in the reflection of the mirror but I just assumed it was Charlie checking on her, which we know he did frequently in the book
Crew or equipment visible: During Edward and Felix's fight, the harness Edward is wearing under the robe is visible in some shots.
Continuity: When James bit Bella in the first movie, 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. I'm still confused as to why the scar looks to be in different places all the time
Continuity: In the meadow with Laurent, the way Bella's hair is hanging changes multiple times throughout the scene, going from untucked to tucked-behind-her-ear and back again, even though Bella does not touch her hair and there is no wind.
Continuity: When Bella is asking Alice where to find Edward in Volterra, she starts the conversation in close-up standing inside the Porsche's passenger door, but when the shot pans out, Bella is standing on the outside of the car's door.
Continuity: At Bella's birthday party, all of the Cullens except for Esme are pale. Esme has the skin tone of a human being.
Continuity: When Bella finds Jacob in the rain, she slams her car door and it doesn't shut fully. The next scene you see the car shut completely.
Revealing mistakes: When Bella is in bed sleeping, and she's screaming because she's having a bad dream. You can clearly see in one shot the actress in the bed is not Kristen Stewart.
Continuity: In the scene where Bella goes to the meadow, her hair is wavy and more tousled, but when Laurent arrives, her hair is noticeably straighter.
Continuity: When Alice takes the photo of Edward and Bella at the party, she clearly takes it with the camera horizontally. However, when Bella prints off the photo, it is vertical.
Factual errors: 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 1st and she had spent at least a month or so working on the bikes with Jacob).
Revealing mistakes: During the fight scene in Volterra between Felix and Edward, you can see bits of blue screen around their arms and hands.
Errors made by characters (possibly deliberate errors by the filmmakers): When Edward parks at school toward the beginning of the film, he parks sideways through multiple parking spaces. (This is especially apparent later in the film when Bella imagines him walking out of his car and it disappears, revealing rows of white lines indicating a different designated parking pattern.)
Continuity: After Bella falls off the motorbike, she gets a nasty cut on her head. In the following scenes, the cut has completely vanished. Yeah I definitly didn't even realize that later on, Bella had no cut on her head
Revealing mistakes: When Bella goes to LaPush in the rain to confront Jacob, she parks her truck and gets out. However, when she tries to slam the driver's door, it bounces back open. Def saw that one
Incorrectly regarded as goofs: 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. However, her immunity is to powers that effect the mind, whereas Jasper's powers effect emotions.
Errors made by characters (possibly deliberate errors by the filmmakers): In the scene where Edward wishes Bella a happy birthday in the parking lot she states that he is a hundred and nine, which is incorrect. He was born in 1901 which would make him a hundred and eight.
Continuity: In the scene wear Jacob climbs through the window to visit Bella in her room she is wearing a tan/white long-sleeve shirt. In the morning when she wakes up her shirt is green. I noticed this one
Factual errors: Bella and Alice fly from Seattle to Italy on a Virgin America Airbus A320. Virgin America only flies domestic flights within USA.
Incorrectly regarded as goofs: 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.
Continuity: In the very beginning when Bella wakes up with the Romeo and Juliet book next to her, the book disappears and reappears between shots while she's talking to Charlie.
Continuity: Through out the entire movie the scar on Bella's arm from James appears and disappears.
Continuity: At the end of the film, when Edward and Bella are in his car after the vote at the Cullens, the aerial view shows they are driving along a long straight road, but when the camera cuts to their faces, the view out of the rear window of the car shows they have travelled along a winding road.
Continuity: During the Edward and Bella break-up scene in the forest, Bella's hair switches from all hanging down her back to some of it being brought forward over her shoulders. In the first shot from behind, it is clearly all fanned out across the back of her jacket, but despite her not appearing to move, in the next shot from behind, the right half of her hair is hanging forward over her shoulder.
Continuity: At the birthday party at the Cullens, Rosalie gives Bella a wrapped present telling her it's a necklace, but Bella doesn't open the present, or appear to put it down anywhere before Alice passes her the present from Emmett, which Bella is holding with both hands when she shakes it
Continuity: 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.
Continuity: 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.
Continuity: As Edward, Bella and Alice are being escorted to Aro by Jane, Felix and Demetri, Bella is walking on Edward's left - however, as they enter the Volturi chamber, she suddenly appears to be on his right.
Incorrectly regarded as goofs: While Bella is having flashbacks of her and Edward lying in the meadow, her left foot appears to be missing but it is only tucked under her right foot.