Plot hole: At the theatre in the "King Homer" bit, the audience are treated to a traditional showgirl spectacle. But the girls have no curtain behind them, and so the audience should have seen Homer the ape, but they act completely surprised a minute later when Homer comes on. (00:11:40)
Plot hole: When Bart prank-calls Moe and tells him his name is Jimbo Jones, Bart says that he lives at 1094 Evergreen Terrace instead of 742 Evergreen Terrace, where Jimbo and Bart are. If Moe had taken those directions, he wouldn't have arrived at the house, instead he would have gone somewhere different. (00:18:30)
Plot hole: In the car chase, Chief Wiggum says that one of the suspects (Marge) "is wearing a green dress, pearls, and a lot of blue hair." However when we see Marge from the police car all we can see is her hair, so how would he have known about the pearls and dress?
Plot hole: When Homer is seen at work in the flashbacks (before Maggie was born), he is at his usual control panel in sector 7-G, but he only began working here when Burns made him safety supervisor in season 1, "Homer's Odyssey". Before Maggie was born he should have been working at the conveyor belt with the carbon rods, where we saw him in the first couple of episodes.
Plot hole: When Bart locks Principal Skinner and Mrs Krabappel in Skinner's office, and tells them that they can't come out until they've reached an agreement, why didn't Skinner and Krabappel just climb out Skinner's office window instead of spending hours pounding on the door yelling to be let out?
Plot hole: In the scene where Bart has to choose the right Roman numeral door in order to avoid the tigers; right as the Shelbyville kids come bursting through the outer door, Bart picks the right door through humorous deduction and escapes. However, the Shelbyville kids are unable to open the door which doesn't make sense, since there is no lock on the door and there wasn't any mention of Bart blocking or sabotaging the door because only a few seconds later we see him on the street continuing to fret about the lemon tree.
Plot hole: The director of Radioactive Man says to Bart "we found our new Fall Out Boy. That's what I would say if you weren't an inch too short. NEXT!" But Milhouse is the new Fall Out Boy, and he's blatantly smaller than Bart. Bart was standing right next to Milhouse, so the director could see the difference.
Plot hole: In "Life's a Glitch", Lisa finds out that she has a seat on the spacecraft going to Mars as the proofreader. How, though, was she not informed of this before going to the rocket? The family only finds out about the rocket after finding Krusty's letter/invitation and the fact that she was on the list there would be no reason why she wouldn't have been informed of this. It was still New Year's Day so if it had been by mail then it would have to arrive before the New Year so as to make the plan work, being as it was a public holiday and no mail would be delivered. Therefore it would have to be delivered personally or someone would need to contact her. There were also many well known celebrities and figures ready to board the rocket. I can't imagine they were all home in time to gather their mail and were all somehow contacted, yet Lisa was simply walking around town and at church and they couldn't find her? There was also no evidence to suggest anything would have stopped her from either receiving the invitation in time or being informed of the mission.
Plot hole: In the last part of the episode, when Mr Burns is trying to convince Homer on his float to play a big prank, the timing is totally wrong. Firstly, Lisa sees the writing 'Happy Pranksgiving' on the side of Mr Burns' float way before it reaches her, and it takes Mr Burns ages to change into the Father Christmas outfit.