E-I-E-I-(Annoyed Grunt) - S11-E5
Plot hole: When the Simpsons run away from the duel, they go to Homer's childhood farmhouse. But Homer and Grandpa burned the farmhouse down in the episode "Grandpa vs. Sexual Inadequacy".
Plot hole: It is shown that Marge first met Luann van Houton when she was ten. But in "Homer Defined", Marge said that she first met Luann in an emergency room when Bart and Milhouse drank paint.
And Maggie Makes Three - S6-E13
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: 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.
Margical History Tour - S15-E11
Plot hole: During the Mozart skit, Lisa puts a sleeping tonic in the emperor's wine, but when she drank it she fell asleep also. How could that be if she only poisoned one glass of wine and it was the emperor's?
Much Apu About Nothing - S7-E23
Plot hole: At the end Apu finds out he's been chosen for jury duty for the first time. However, in 'The Boy Who Knew Too Much' he was on the jury.
Plot hole: A little ways into the episode, when Milhouse kisses Homer, he says that was the first kiss in his whole life. However, we see him kissing Samantha Stanky in the episode "Bart's Friend Falls in Love," in Season Three.
Diatribe of a Mad Housewife - S15-E10
Plot hole: Dr Marvin Monroe says to Marge he was gone for a long time because he was sick. That's impossible because he died in a previous episode and you can even see his tomb in the episode where Maud Flanders dies. [It could be argued that Monroe really was sick. It was never explained how he died and no one mentioned that he really was dead. The grave, the hospital named after him were in the simpsons universe with the belief he was dead. The clip show mentioned his death but alluded any specifics. As Marge mentions she thought he was dead and so could everyone else on the show.]
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: 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.
Mr. Lisa Goes to Washington - S3-E2
Plot hole: The Simpsons take a flight to Washington D.C. for Lisa's speech. But it is revealed in a later episode that Marge has a Fear of Flying. This was before it was discovered that she had a Fear of Flying.
Dude, Where's My Ranch? - S14-E18
Plot hole: Lisa says Luke was her 1st crush. What about Nelson, Corey, Mr. Bergstrom, Thelonius and the boy that works at the library in 'Bart's Girlfriend'?
Suggested correction: She didn't have much of a crush on Mr Bergstrom, she mainly admired him because he was kind. However you are correct about the others.
Plot hole: When they are sitting around the campfire, Lenny says that the nuclear plant has only just opened. But in another episode where Homer is in high school, the guidance counsellor tells him that the power plant will soon be opening.
Marge vs. the Monorail - S4-E12
Plot hole: When Homer is trying to stop the Monorail, he grabs the big M from the side of the train and uses it as an anchor. However, when the M cuts through 'Springfield's Oldest Tree', there is no visible monorail track or supporting pole in the background.
Diatribe of a Mad Housewife - S15-E10
Plot hole: When Marge is looking for inspiration for her novel, she looks at the boat painting in the TV room. On the frame, she reads it and says: "Scene from Moby Dick". Yet in "The Trouble With Trillions", Marge said that she painted it herself for Homer. So then why would she have to read the label to find out where it's from if she painted it?
Plot hole: If there were too many people in the shelter when Homer was trying to shut the door, how could Ned easily walk up to his family and then outside?
Plot hole: Marge pops her shoulder out of place curling. Yet in the next scene she's seen with a wrist cast. (01:15:30 - 01:16:15)
Tree House of Horror X - S11-E4
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: 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: 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.