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: To rig blackjack card shuffling machines to make the dealer bust and everyone else get 20 or 21, its success would depend entirely on knowing the exact number of people at the table at that time. Perhaps the filmmaker is assuming all seats at the high-stakes blackjack tables would always be filled during a "soft" opening, but that seems extremely unlikely.
Plot hole: Vanessa seems upset at Barry when their actions at getting the honey back from the humans result in the flowers and other plants dying. One might think that Vanessa, as a florist, would know the outcome and would warn Barry instead of helping him with his plan. Yet she appears to blame him for the entire outcome when it becomes apparent.
Plot hole: In the scene with the brothers group, the guys don't believe that Fred is Santa Claus's brother (because they don't believe in Santa). But why don't they believe in Santa? Santa leaves gifts for kids on Christmas. If they don't believe in Santa then where do they think the presents came from?
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 everyone is passing the bill and Evan's suit changes to the robe, how is it that no one noticed that he came in wearing normal clothing and then his clothes changed into the robe in less than a second. Heck it showed his family watching him walk right into the room wearing normal clothing, and then watched him the entire time. How did they not notice that he never once changed his clothes?
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: When the chipmunks finally release their first song, there is a montage showing the chipmunks rising musical success. In one shot we see a marquee promoting "The Chipmunks Premiere CD Release", and on it is a picture of the chipmunks in the clothes Dave has made them (note Alvin in his 'A' jumper.) However, Dave doesn't actually make the chipmunks these clothes until further on in the film. (00:41:50)
Plot hole: Reverend Frank reveals that he once married an immigrant from his congregation so that she could stay in the country after her application for asylum was rejected. No immigration official would ever have believed such a marriage (to a priest!) to be genuine and her application of leave to stay would have been rejected.
Plot hole: There are two cars driving behind the EPA truck containing Marge, Bart, Lisa and Maggie. When Homer uses the bulldozer to try and break the family out of the truck, the two cars behind the truck don't notice the bulldozer trying to destroy the truck. There's no way they couldn't have not seen the bulldozer since they were just behind it. (01:00:05 - 01:00:40)
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.