Continuity mistake: When the Simpsons are driving to Cypress Creek the arrangement of luggage on the roof of the car changes depending on their stage in the journey.
Tree House of Horror XII - S13-E1
Continuity mistake: When the family finds Homer, he has an hole behind his head and you can see his brain, but it's not there later.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Homer walks up The Front drive you can see the road and there are no markings on it. But when he turns to look at his house, there are orange lines running down the road. (00:08:50)
Continuity mistake: When Homer is on stage in Springfield and preparing to get hit by the cannonball, the speaker-tower, behind and slightly to the left of him, completely disappears in the wide shot right before Homer jumps off stage.
Raging Abe Simpson and His Grumbling Grandson in 'The Curse of the Flying Hellfish' - S7-E22
Continuity mistake: At Asa's funeral Burns and Grandpa both produce a key to unlock the compartment in the Hellfish monument, but even though they both take their keys out of the keyholes after turning them, all 9 keys are in place in the following shots.
Continuity mistake: When Marge arrives home complaining that she is too tired to talk, there is an alarm clock on Homer's night table. When first shown it is a black electric clock, but when it is shown in the very next scene, it is an old orange one. Only a few seconds passed between these scenes, meaning there was no time for anyone to change it.
Continuity mistake: When Bart and Lisa wake Homer and Marge up in the morning of the Duff Gardens visit, the kids are standing by the bed. However, when Marge throws the mouldy sandwich in the bin in the next shot and Homer collapses, the kids have disappeared. In the next shot, they are back again.
Bart Gets Hit By a Car - S2-E10
Continuity mistake: In Moe's Tavern, in the close-up of Marge as she says "Homer, look at me" the glass window behind her has a different pattern than in all the other shots (2 rows of red tiles instead of 3).
Continuity mistake: When Homer is at the retirement party, there is a far shot of him (when Smithers talks to Mr. Burns) and he isn't wearing his jacket. In every other shot Homer is wearing his jacket. (00:05:20)
Brake My Wife, Please - S14-E20
Continuity mistake: Whilst Bart is having breakfast he pours a lot of maple syrup onto his pancakes. When Marge walks into the kitchen to hurry him up the syrup on his pancakes has completely disappeared.
Dude, Where's My Ranch? - S14-E18
Continuity mistake: When Lisa meets Clara, there is a close up of her necklace. The necklace is never there in any of the other shots that we see her. Her ring, as also seen in the close-up isn't visible either.
Continuity mistake: The letter Bart receives from Edna reads "94 Evergreen Terrace," however in other episodes they live at 742 Evergreen Terrace. (00:08:45)
Diatribe of a Mad Housewife - S15-E10
Continuity mistake: During the "performance" at the end of Marge's book, "Ned" is skewered by a harpoon and falls off the cliff. When "Homer" walks up to the cliff edge you can no longer see the rope trailing from the end of the harpoon. However, moments later he gets his leg caught up in it and is pulled over himself.
Bart Carny - S9-E12
Continuity mistake: At dinner when the carny dad is doing his cigarette trick, the shot changes to Bart and Lisa and they have piles of food on their plates. About 10 seconds later Marge gathers the plates up and there is nothing on them. Are we to believe that they ate all this food in such a short space of time?
Continuity mistake: In Moe's, Homer points at Lenny and says "Are you calling me a liar," with the same hand which is instantly holding a beer in the next shot.
The Old Man and the Key - S13-E13
Continuity mistake: After Homer's father, Abraham, comes home after a night out with Zelda, Homer snatches his keys away from them. He leaves his hand out and begins outstretching fingers one by one to represent all the people he called in worry, and it's clear that the keys have disappeared.
Continuity mistake: When Marge and Ruth and shooting cans, there are five on the fence, then, in the next shot, there are only four.
Continuity mistake: When the angry mob smash all the statues and the fountain before the song, during the song you can see all the statues and the fountain intact.
Continuity mistake: When Homer hands over the key to Mayor Quimbey, the mayor points out the teeth marks on it. But in the next shot when Homer says he thought there was chocolate inside, the bite marks are gone. (00:16:30)
Continuity mistake: When Flanders walks up to the door, there is nothing next to the door, but in the next shot after Homer has thrown garbage onto him, there is an egg box next to the door.
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