Tree House of Horror XII - S13-E1
Continuity mistake: In 'Hex and the City,' as they walk through Ethnictown, Marge has a handbag over her shoulder. But in the closeup when she says "Oh, listen.", the bag has gone. (00:01:15)
Continuity mistake: When Krusty the Clown arrives at the beauty pageant his tie is done up. When he goes on stage it is undone.
Continuity mistake: When the Repo Man takes Marge's ring, we see the ring on her left hand. It wasn't visible in the shot before. (00:14:40)
Tree House of Horror III: The Simpson's Halloween Special III - S4-E5
Continuity mistake: When Homer is escorting his family out of the house to escape the Zombies, he leaves the door wide open, but in the very next shot it is shut. (00:18:50)
Continuity mistake: While Bart starts the I.Q. quiz and is reading it out loud, his teacher says "Shh. Visualize it Bart." While this happens if you look in the background you can see the alphabet line. It starts out Tt Uu Vv Ww, then Bart's teacher blocks out some, then you see the letter T again. (00:04:50)
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: At work, the salad in Homer's sandwich disappears when he mentions that 'she' made it.
Continuity mistake: When the pile of newspapers fall on principal Skinner, two garbage cans appear out of nowhere beside the door. (00:19:10)
Bart Gets Hit By a Car - S2-E10
Revealing mistake: After Marge has been in court, Mr Burns' lawyer says "Thank you very much Mrs Simpson", and when he does it, the top of his head above his glasses is less pale than the rest of his face.
Treehouse of Horror XV - S16-E1
Continuity mistake: At the beginning when Kang and Kodos's boss comes to have dinner, his stomach explodes leaving a hole, yet in the next shot the hole has vanished. (00:00:40)
Continuity mistake: After Homer dodges the cannonball near the end of the episode, the blue platform that he stood on goes further away from the edge of the stage between shots, and when Homer hugs Marge the platform has disappeared and Peter Frampton's cooler has become closer to Homer.
Tree House of Horror V - S6-E6
Continuity mistake: In 'Time and Punishment,' when Homer exits the basement, he discovers Bart and Lisa are giants, and he then screams and runs back to the "basement" - however the same door that leads to the basement seconds ago, now leads to a green -carpeted room, and the basement seems to have vanished. The door is also hinged on the wrong side. (00:12:50)
Continuity mistake: When Homer sulks on the couch, he has a pillow under his head, which is pink. In a closer shot, the pillow turns light blue, but in another shot, the cushion has turned pink again. (00:17:10)
Continuity mistake: When Homer and Bart are at the cabaret show, Mr. Burns and Smithers are there with two women. In almost all of the shots there is a woman sitting between Burns and Smithers, except in the close-up of them when Burns asks "How does he DO it?". Then Smithers is shown as sitting right next to Mr. Burns. (00:21:00)
There's No Disgrace Like Home - S1-E4
Continuity mistake: As Homer is carrying the TV towards the pawn shop in the first shot the left window is clear. There is then a tracking shot of the family walking and when they get in front of the store the window has writing on it saying Pawn Shop. The writing is in black and the next shot when they are talking the writing is now dark brown. (00:14:20)
Continuity mistake: The photo Edna sends to Bart differs when he shows his parents. The angle is different from what it was previously, revealing part of a photo frame on the wall which wasn't there before, and the sheets/pillows on the bed are different, and her eyes are closed when they look at it, but when Bart looked at it, they were open. (00:09:05 - 00:18:25)
Home Away From Homer - S16-E20
Continuity mistake: When Homer rings the doorbell of the Flanders' former house to visit the new neighbour, it moves downwards on the door frame. In the first shot it lines up with the gap between the lock and the doorknob, but in the next shot it is beside the doorknob, and in other shots in the episode the doorbell isn't even there. Also, the glass panels on both sidelights line up with the door differently between shots.
Revealing mistake: At the car convention, Homer chides Bart through the windscreen of Bonnie and Clyde's car. However, Homer's body is not seen through the holes in the windshield, which shows that the holes in the windshield were achieved via a layer of red-coloured holes. (00:04:25)
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.
Tree House of Horror V - S6-E6
Continuity mistake: In 'Time and Punishment,' Homer goes back in time, then returns, and the kitchen table has plates of food, cutlery and glasses all set out. Then when Homer is informed that Ned is the Lord of the Universe, the house starts shaking, but you can see the table is now totally clear. (00:11:15)
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)
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