It's mentioned a couple times that Riley (as a human) has been missing for over a year. But when Charlie is looking at the Missing Persons flier, it says Riley was last seen in May 2010. (The movie clearly takes place in June 2010, as evidenced by newspapers with current headlines regarding the vampire attacks in Seattle.)
During the training fight scene when Emmett is sparring with Jasper, Emmett throws a punch at Jasper with his right hand (as they meet in battle again after Emmett threw Jasper), but in the transitioning scene when Jasper ducks, Emmett is punching with his left hand.
when Edward is fighting Victoria and Riley, Bella cuts her arm with a rock. when you see the blood run down it clearly shows that she had cut under her sleeve, but when Edward goes to wrap her arm he wraps around close to her wrist. This is not near where the blood came from.
When Bree is first leaning up looking at Felix when he is heading towards her, she is leaning up with her hair un-tucked from behind her ears. But when the next camera shot goes back to her, she is laying back on the ground with her hair tucked behind her right ear.
During the scene where the Cullens are watching the news, the woman says "reporting live". She's in Seattle and it's night time there but at the Cullens' house we can see it's day time (through the window). Forks and Seattle are in the same time zone, therefore it should be the same time of the day in both places.
When Jasper is telling Bella about his past, he states that he was in the Texas Cavalry and was heading to Galveston before being turned. The scene cuts to this action, showing Jasper riding a horse with mountains in the background, and then in front of the ocean. There are no mountains within several hundred miles of Galveston, Texas.
If Edward spent most of his senior year in Italy, how was he able to graduate on time? In the novel, it is revealed that Edward was smart enough to earn extra credits for all he missed as well as being able to put his persuading skills to the use.
In the tent scene Jacob has to come in to keep Bella warm because it is so cold. The next morning she is outside in jeans and a button down shirt with the sleeves rolled up, not coat, no hat, no gloves. However, the temp in daytime snow is far different from the overnight temps in a driving blizzard, and it's entirely possible that Bella is comfortable without a jacket.
When Jacob shows up at Bella's school his hair appears to be wet and lying flat. However when he and Bella arrive at Sam's house his hair is fully dry. Since it is about a fifteen to twenty minute motorcycle ride from Forks to Sam's house on the reservation and Jacob doesn't wear a helmet, it is completely possible that his hair dried in the wind on the way. Also, his temperature (and therefore his head) runs very hot, which may have helped speed up the drying since his hair is very short.
When Jacob pulls up to the school, the license plate on his motorcycle is for California when the movie is supposed to be set in Washington. However, Bella states that she saved the motorcycles from the trash. Since she got them used, we have no way of knowing where the original owners purchased them. It is highly doubtful that two teenagers would've bothered to properly re-register them and get fresh plates and tags.
In several scenes (i.e., at the lunch table when the graduation party is 1st being discussed), some sort of "tape" or "adhesive" is visible under the Cullen Crest on Alice's necklace, obviously to hold it in place during movement.