Continuity mistake: When Maya and Moe arrive at Moe's house, you can see there is nothing on the arm of the sofa, but in the next shot a remote control appears from nowhere.
Continuity mistake: When Moe is sorting out the flowers at Moe's bar, you can see there is nothing behind the beer taps on the counter, but in the next shot a jar of pickled eggs appears from nowhere.
Continuity mistake: When Maggie is swinging a spade at the other children in the playground, there is a tree behind her that disappears in the next shot.
Continuity mistake: When Homer is pushing Maggie along in her pushchair, Santa's Little Helper comes along and you can see that Maggie has a dummy in her mouth. In the next shot, the dummy has disappeared.
Continuity mistake: At the beginning of the episode, the doormat outside the Simpsons' house is green, but when Maya and Moe arrive at the Simpsons' house for their double date later on, the mat is now purple.
Continuity mistake: When Homer says "I will never know the score!" the bag of chips turns from green to blue.
Revealing mistake: At the craft store when Homer and Bart go in, the door opens before Homer pulls the handle. (00:14:00)
Waverly Hills 9-0-2-1-D'oh - S20-E19
Revealing mistake: In all the intro scenes from season 2 to season 20, episode 19, in the wideshot where Bart skateboards out of the school, if you look closely, part of the sky can be seen on the ground. (This mistake may only apply to the original format).
Other mistake: When Homer throws his beer bottle in the air and puts the gun in his mouth, the beer bottle never lands. (00:15:30)
Character mistake: When Maggie starts speaking Ogdenvillian, Marge says that it is her first word. But in the episode "Gump Roast", everyone, the Simpsons included, all watched a video of Maggie saying her first word. (00:17:35)
Continuity mistake: When the wall is fully built, the people who put the wall up are several feet away from the rest of the people there. In the next shot, everyone is standing together. (00:19:20)
Continuity mistake: When the fence between Springfield and Ogdenville is put up, Marge can be seen in a crowd behind all the people putting the fence up. In the next shot, Marge is next to the crowd of people who put the fence up. (00:19:20)
Continuity mistake: When the police arrive at the gate, Chief Wiggum is in one car and Lou and Eddie are in another car. But in the next shot, Chief Wiggum and Eddie are in the same car. (00:20:00)
Revealing mistake: While Lou is talking to Chief Wiggum about having his belt stuck to a street sign, Lou's mouth disappears for a single frame.
Audio problem: When Matt Groening is putting boxes of comic books into the Comics Bongo Group truck, he says "I'm so rich" but his mouth isn't moving. (00:04:40)
Audio problem: When Homer says "I need change for a dollar. I also need a dollar", his mouth doesn't match what he's saying. (00:07:25)
Continuity mistake: Ms. Krabapple takes the cellular devices from the children in her class and puts them in a Laramie Cigarette box. She dumps the box into a desk drawer filled with frogs. A few seconds later there is a shot of the class from her point of view with all of their cellular devices on their desks. (00:03:00 - 00:08:15)
Continuity mistake: The size of the smiley face on Krabappel's mug keeps changing between shots. (00:04:50)
Continuity mistake: While Edna is holding the "Goddess Bar", her shirt sleeves are pink like her pyjamas, but in the next shot, she is wearing her usual green outfit.
Continuity mistake: Barney is simultaneously seen at the wrestling stadium watching the fight, and at Moe's.
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