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.
Lisa's Rival - S6-E2
Continuity mistake: The position of Ralph's Star Wars action figures changes the two times they show his diorama.
Other mistake: There are two mistakes when Bart calls the Krusty Hotline: 1, The cereal box says the phone number is '1-909-O-U-KLOWN.' Bart presses eight buttons on the phone. 2, as he is dialing, you can HEAR seven buttons being pressed. (00:01:45)
There's No Disgrace Like Home - S1-E4
Other mistake: When Homer is at Moe's, there is a boxing match happening on TV. There is a bald guy who is getting considerably battered by the opponent and gets knocked out, and then for some absurd reason he is victoriously standing and smiling as if he had won.
Continuity mistake: When there is a zoom in of the house just before Bart gets up late, it has the old arch-shaped windows, but in the rest of the episode it has the normal windows. It's obviously a screen from Season 1. (00:06:00)
Large Marge - S14-E4
Factual error: In Luigi's, the lobsters in the tank are bright red. They are actually quite dark brown until they are boiled when they become red/pink.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: During the family's breakfast, in most shots Marge sits right beside Maggie's highchair, but in certain close-ups they are quite a few feet away from one another. (00:05:25)
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: The shot glass that Burns places on his desk disappears for several frames before reappearing. (00:05:45)
Tree House of Horror XII - S13-E1
Audio problem: In Reaper Madness; the scene where Homer destroys the Grim Reaper with a bowling ball, Bart is pinned on the wall by the Reaper's scythe. The scythe disappears and Bart says "Cool!" but his mouth just opens up and doesn't match the word.
Continuity mistake: When we first see Homer feeding the can to the goat the background shows a wooden coop. In the next shot, a purple tree stump appears there too.
Continuity mistake: When Homer shows his "incriminating photos," you can see that in them, he is bald. We know from several previous episodes that Homer had hair when Bart was a baby. He even has a bit of hair when Lisa is born.
Continuity mistake: At the end, the barriers outside the tavern change position. (00:21:00)
Continuity mistake: The bible that Reverend Lovejoy returns at the library is bigger in the first shot.
Continuity mistake: At The Town meeting Mayor Quimby's tan disappears in the middle of the scene.
Homer's Triple Bypass - S4-E11
Other mistake: In the beginning of the episode when Chief Wiggum orders a battering ram through The Front door of a house, Reverend Lovejoy opens the door and questions what they are doing. Chief Wiggum says "isn't this 742 Evergreen Terrace?" to which Lovejoy replies that it's the house next door. In the next shot, you see Snake pulling out of the garage and speeding away. Everybody knows that 742 Evergreen Terrace is, in fact, the Simpson residence. (00:02:40)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: In the bar, before Bart stomps on Mr. Burns' foot, his back is toward Smithers, but in the next shot, his back is turned toward everyone else. (00:19:15)
Moaning Lisa - S1-E6
Continuity mistake: When Homer says "I can't concentrate with that infernal racket", the shot goes up onto Lisa's room. From the outside, there is no window frame on the window. But from the inside, there is one going right through the middle.
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?
Continuity mistake: When Judge Harm is yelling at Marge and Homer after they have cut the rope, Marge is wearing lip gloss, and between two shots, it disappears.
Mr. Spritz Goes to Washington - S14-E14
Audio problem: At the end of the episode, when the guy who helped the Simpsons pass the bill says, "I just passed a bill in three hours. Quit complaining," his mouth movements don't match the words.
Answer: I'm not sure if this is the one you're thinking of, but an episode of "Ray Bradbury Theatre," called "A Sound of Thunder," dealt with a similar matter: a group of hunters travel back in time to hunt dinosaurs, only to find things have changed when they get back because someone stepped on a butterfly.
Xofer