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).
Sex, Pies and Idiot Scrapes - S20-E1
Continuity mistake: When Homer has Snake cornered, the second rung on the ladder behind them is broken. In the next shot it's not broken, then it is again.
Continuity mistake: In the scene where Moe is cleaning his window inside the bar, take notice that the size of the spot he cleans on the inside of the bar is small. But when the shot changes to the outside, with Moe and the others looking out from the inside, the clean spot is larger.
Continuity mistake: As Marge is feeding Maggie a grapefruit, Bart takes out his bongo drums and plays them. Watch as Bart plays - the shot zooms in from the back of Bart towards Maggie, and you can't see Marge in the scene sitting close to Maggie; the next shot shows her though.
Continuity mistake: When Maya and Moe are at Moe's home, Maya gives Moe a glass of water and he sits down on the sofa with the glass in his left hand. In the next shot, the glass has gone.
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: When Alberto says "If you had completed your seduction of me, I never would have met Sylvia," his shirt collar briefly turns into the same color as his blazer.
Continuity mistake: In Bart's room, while Lisa is carrying the Krusty phone, the back of the phone Krusty's neck changes from white to yellow multiple times in the same shot.
Sex, Pies and Idiot Scrapes - S20-E1
Continuity mistake: During the St. Patrick's Day parade, Bart is wearing a green shirt throughout the whole scene, but he's wearing his usual orange shirt when he says "Where's the IRA when you need them?"
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.
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)
In the Name of the Grandfather - S20-E14
Continuity mistake: When Grandpa smashes the hot tub, the pieces from the hot tub disappear moments later. (00:05:25)
Mypods and Boomsticks - S20-E7
Revealing mistake: When Bashir leaves the Simpson house, he doesn't have any eyebrows. (00:12:40)
Mypods and Boomsticks - S20-E7
Continuity mistake: When Homer runs into the old Springfield Mall at the demolition, if you look closely you can see Hans Moleman there. However, when the Duff truck crashes and Homer swims to save the beer, Hans Moleman is now in the truck. (00:18:30 - 00:19:05)
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)
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