Continuity mistake: Before Krusty is arrested, he grabs a drink and there is no olive in it. When he sits down, an olive has appeared in the drink. (00:05:35)
Kill the Alligator and Run - S11-E19
Deliberate mistake: When Marge is sweet talking the sheriff, Bart unlocks all but Homer's foot chains, but when they're running for the gate, Marge, Bart, and Lisa's shackles can be seen.
Continuity mistake: When Homer says to Bob that he tells Marge everything, his hand is by his mouth, the shot cuts and it is at his side.
Margical History Tour - S15-E11
Factual error: On the castle where King Henry VIII is supposed to live, the flags at the top have the pattern of the English flag, being a + shaped cross on a coloured background, but it should be a red cross on a white background. Instead it's a white cross on a blue background. Those are the colours of the Scottish flag, but England and Scotland were separate countries at that point in history. And the cross on the Scottish flag is an X shape rather than a + shape anyway.
Team Homer - S7-E12
Continuity mistake: When Moe says Mr. Burns is going to have an accident, he's wearing his pin pals shirt. When Moe hits Mr. Burns, he wears a mask and different clothes. Moments later, when talking to his bowling team again, he's back in his pin pals shirt.
Continuity mistake: In the new opening sequence, Kearney and Dolph cut off Jebbidah's head. But in the pan of the city, the head is back.
Continuity mistake: Towards the end, when the scientist is trying to give everybody diamonds, a shot cuts to just Marge and Lisa, but out of nowhere Maggie appears. (00:19:30)
Continuity mistake: When Homer is shot at the hippie farm, he ends up with a flower in his head, stem first. But he put the flower in the gun barrel stem first, as well. From a shot at that close a range and that velocity, there's no way the flower could have turned around in mid-air.
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.
Audio problem: In the scene where Lisa is presenting her bully repellant at the 'Big Science Thing', when she first walks onstage there are murmurs of disapproval among the scientists, in which you can hear one of them saying, "Let's not listen". But after Lisa sprays the repellant on herself and stops Francine in her tracks, the scientists start murmuring in astonishment. However, if you listen closely, you'll hear the same recording of someone saying, "Let's not listen".
Continuity mistake: When the Simpsons are on the raft going down the river in Africa they come to a fork and have a choice of going to the left, towards a sunny and nicer area or to the right where it is rainy and gloomy. As Homer tries to steer the raft to the left as he pulls his left arm out of the water and it is covered in leeches but in the next shot of him when we see the arm again the leeches are gone. No way to remove leeches that fast.
Other mistake: When Homer is being interviewed while feeding baby Lisa, there's a picture of 8 year old Lisa in the background.
Continuity mistake: Patty and Skinner go to see 'Space Mutants IV: The Land Down Under'. In a season one episode, 'The Telltale Head', a sign on the Springfield Aztec movie theater reads 'Space Mutants IV: The Trilogy Continues'.
Home Away From Homer - S16-E20
Continuity mistake: We see Coach cutting down trees in Flanders' former driveway. However there had never been any trees in Flanders' driveway.
Lisa's Pony - S3-E8
Continuity mistake: The number of knives that Sherri is holding changes between long and close shots at the talent show. (00:04:50)
The Old Man and the C Student - S10-E20
Audio problem: At the choir at the start, Lisa's lips don't move when she says "oh no."
Audio problem: When princess Kashmere is introduced, we hear Homer laughing, however we see him eating and not opening his mouth. (00:08:00)
Tree House of Horror X - S11-E4
Character mistake: When the Collector is putting Lucy Lawless into her plastic bag in his lair with the other celebrities, he refers to Tom Baker as "Doctor Who." As a sci-fi nerd, he would know the character's name is simply "The Doctor."
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: When Homer is at the vending machine, in certain shots he is wearing a tie and in others he isn't. (00:02:20)
Smoke on the Daughter - S19-E15
Audio problem: When Martin runs with his book when Kirk Van Houten says to Otto "It's for my kid." he shouts "Eureka!" but his mouth says something completely different.