Continuity mistake: At the Penitentiary, Jimbo's video camera appears and disappears from nowhere. He isn't seen carrying it on him.
Continuity mistake: When Homer jumps in the car having completed the Fatherhood test and drives off to see Bart race. The car shifts from reverse to forward without Homer moving a gearstick. (00:18:40)
Homer vs. Lisa and the 8th Commandment - S2-E13
Continuity mistake: When Homer is sitting watching cable, the rest of the family comes home and one of them is carrying a plant in a pot, which is put down next to the couch. While they watch and watch cable, it grows very tall and then withers down. When Homer goes behind the TV and starts kissing the wires, the plant has moved to next to the doorway and is suddenly fully grown again.
Tree House of Horror VII - S8-E1
Continuity mistake: In 'The Thing and I' when Homer and Marge return from driving around in the rain, there is no doorknocker on the door. Then in the shot where Hugo escapes, we see the door open with red scratches on it, and there is a doorknocker. Then later when everyone leaves to find Hugo, it's gone again. (00:02:40 - 00:04:55)
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: When Bart is unpacking his things from the box, if you look at the mantelpiece, we can see that there is a candle on the right hand side of it. But later on, there is a candle on the left hand side which wasn't previously there. (00:02:30 - 00:03:15)
When You Dish Upon a Star - S10-E5
Continuity mistake: In the shot just before Alec gets hit by a tree branch, his watch is missing but in the next shot, his watch gets snagged on something.
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When Maggie is driving Homer's car, a man is behind him. He is seen waving his left arm but when the shot changes to Maggie he is waving his right arm. (00:14:50)
Continuity mistake: When Homer is having the thanksgiving dinner at Moe's, he isn't wearing a tie, but between shots he suddenly gains a tie. (00:20:35)
Continuity mistake: When Lisa starts to drive away with Homer's pig, Marge is screaming 'No.' On Lisa's close up we can see Marge briefly to the left of the screen and her mouth isn't shouting.
Kamp Krusty - S4-E1
Continuity mistake: Homer points out to Marge that now that the kids are away, he has grown two more hairs, making it four on the top of his head. Later when they are reading Lisa's letter, he has two hairs again. But later still when they are watching TV, he has four again. Two of them fall out when he see that Bart is the ringleader, leaving him with his original two. (00:15:35)
Continuity mistake: When the Home security seller is first seen, he steals an ashtray and a remote control off a speaker and turntable player both close to each other, When the shot changes the speaker and turntable player are much further away from each other.
Treehouse of Horror XV - S16-E1
Continuity mistake: When Chief Wiggum has been caught, we see him drop his eel pie, then when the shot changes it is not there. (00:13:30)
Treehouse of Horror XV - S16-E1
Continuity mistake: When Comic Book Guy gets stabbed, we see him reaching for a potion, and in the first shot, its a purple liquid with no label on the bottle, and when the shot changes we see it is a green liquid with a label on the bottle. (00:10:20)
Tree House of Horror VII - S8-E1
Continuity mistake: In 'The Thing and I' when Lisa and Bart are questioning Homer about the 'thing' up in the attic at breakfast, Homer is the only one eating. But in the next shot you can see Lisa and Bart with breakfast too. (00:01:30)
The Two Mrs. Nahasapeemapetilons - S9-E7
Continuity mistake: When Apu walks down the isle the early shots show that Bart and Lisa are not amongst those either side.When Apu walks by,the shot goes to the ground and they have now appeared.
Tree House of Horror X - S11-E4
Continuity mistake: While the Simpsons are standing in the line, waiting to enter the rocket to Mars, you can see Professor Frink wearing a white shirt. However when he enters the lift to the rocket, he has a green shirt on.
Continuity mistake: When wedding has been just called off, Lunch Lady Doris calls everyone for wedding cake, and among people who rush to it we can see Moe (you can recognize him by his eyepatch), then, Lisa starts to walk off and among the people she passes by you can see both Lunch Lady Doris and Moe.
Continuity mistake: In the White House, Bart puts his cassette player front towards Lisa, but when Lisa pushes it out, it switches to face Bart between shots.
Homer's Triple Bypass - S4-E11
Continuity mistake: When, Lisa bangs on the window of the operating theatre, there is a person sitting behind her who is asleep. However, when she shouts to Dr Nick, the people behind her are completely different. Then she sits down again, and the sleeping person is behind her. (00:20:00)
Homer vs. the 18th Amendment - S8-E18
Continuity mistake: When Homer and Bart are escaping from the cops after stealing kegs of beer from the dump, they drive through a cemetery and slam into a headstone, breaking the right headlight of the car. When they pull into the driveway back at Evergreen Terrace, the left headlight is the broken one.
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