Plot hole: In this movie Goblin was able to sneak up on Peter. But in the previous movies Peter was able to sense danger from quite a distance away; Green Goblin from a few blocks and the train barricade from over a mile.
Plot hole: The idea that Ben Gates had to run away despite the President's being okay with the kidnapping does not make sense. The President could simply pardon him if necessary. However, when he ran away, he would likely be committing other crimes (fleeing and eluding police, reckless driving, etc.) that would not be federal crimes and so would not be pardonable.
Suggested correction: That's basically what he did at the end. Even though the President was OK with Ben "kidnapping" him, if Ben didn't find the lost city of gold he would have been arrested and charged for kidnapping the President (amongst other charges). However, because Ben was able to find the city the President gave him and his crew a full pardon and explained that it was a misunderstanding.
Plot hole: During the climatic battle in the snow, Lyra Belacqua is about to get shot by one of the soldiers, and Iorek Byrnison comes to her rescue and is able to surprise & kill the soldier. The problems with this is where Iorek appears would have been right in the line of sight of the solider, and bearing in mind that Iorek is VERY big, wearing armour so as not to blend in with the white surroundings, and making lots of noise, it would have been impossible for Iorek to stealthily appear from nowhere.
Plot hole: Harry can now see the thestral creatures because he witnessed Cedric Diggory's death in "Goblet of Fire." However, he should have been able to see the thestrals after Professor Quirrell died from Harry's touch in "Philosopher's Stone". Quirrell crumbles into dust (dying) while Harry is still conscious, watching, and fully aware of what he is seeing, thus allowing it to fully sink into his consciousness. Harry faints "after" Quirrell is dead and as Voldemort's spirit passes through his body. Nor does it only have to be a friend or loved one who dies before the thestrals can be seen - it can be anyone, including an enemy like Quirrell. There only has to be an emotional response to the death, which can be love, hate, fear, shock, etc. (In the book, Harry did not see Quirrell die, but that's irrelevant to the film).
Suggested correction: JK Rowling has said that in order to be able to see thestrals the death has to "sink in" psychologically with the person. Which was her explanation for why he couldn't see thestrals even though he witnessed his mother's death. Given Harry's age and the way Quirrell died, it is possible that Quirrell's death didn't have enough of a psychological impact on him to "sink in." After I first personally witnessed a violent death, I didn't feel the impact until a few years later. It can take time.
Plot hole: Landy uses the code 4/15/71 to point Bourne to the training site address. But how does he know it is on the East side?
Plot hole: At the end, none of the duplicate Benders that are waiting in the limestone cavern under the Planet Express building have had their Obedience Virus or the time code deleted from them. There should have been only one Bender without the Obedience Virus, not all of them.
Plot hole: When Wilbur and Lewis are time traveling for the first time, Lewis says he's done with the memory scanner. Since he said he wouldn't invent Dor-15, and she went away, wouldn't the time machine and everything else in the future go away since the memory scanner started it all and Lewis decided to quit?
Suggested correction: Lewis wasn't fully giving up. He was just frustrated and probably went back to it later anyway. Whereas with Doris, he deliberately decided not to invent her because of the danger she posed.
Plot hole: I can somewhat understand that in a kiddies' show all aliens can inexplicably speak English - but using Terranean (i.e.: Arabian) numbers as well? While Tetrax's computer uses alien runes, the readout on Gluto's holographic HUDs use Arabic numbers - somewhat a bit too deliberate a producer choice to emphasize intergalactic communication.