Continuity mistake: When everyone discovers Milhouse has eaten the food, Milhouse then says "You wouldn't dare hurt me. You forget, I have the glasses." After this line, Nelson takes off Milhouse's glasses. At this point, a rip is visible on the left side of Nelson's shirt. Milhouse then walks backwards and Nelson is seen re-entering the shot from behind Milhouse. Only now, the rip in Nelson's shirt is now suddenly on the right side of his shirt.
Continuity mistake: When everyone sees Milhouse after they find out the food has disappeared, Milhouse's arms are by his head. In the next shot, one of his arms is suddenly on his belly.
Continuity mistake: When everyone notices no food in the cooler, the cooler lid is raised, then it is down, then it is suddenly raised.
Continuity mistake: When everyone takes food out of the cooler, Bart has a bag of OREOs which magically becomes a bag of different cookies.
Continuity mistake: When the kids wash up on the island after the bus falls into the ocean, we can see they are totally dry. But they were just in water a minute ago, so they should be soaking wet.
Continuity mistake: When Homer and Karl are selecting a suit, just after Karl says none of the suits are to his liking, Karl's tie changes from green to red.
Continuity mistake: When Bart and Nelson first roll the orange and apple, we can see there is no-one sitting in front of Nelson. But a couple of shots earlier, we saw Milhouse sitting in front of Nelson.
Continuity mistake: On the bus, Otto rewinds his tape and there is a shot of the kids. In this shot, we can see the kids and nothing else. A couple of shots later, a food box has appeared out of nowhere.
Continuity mistake: When Homer has the Bill Of Rights, he ends up ripping several parts of it. The rips keep alternating between shots. (00:05:25)
Continuity mistake: Mr. Burns attempts to plan revenge on Springfield by placing The Town in a dome. However when Lenny tells Burns it has already been done, Mr. Burns tells the helicopters to stop placing the dome. In this shot, both Burns' helicopter and the helicopters placing the dome are the same height off the ground. But in the following shot, the helicopters are now 50 feet above Burns' helicopter. (00:18:55)
Continuity mistake: The X-rays of Homer's intestine change sides between shots when he is at the vet.
The Wizard of Evergreen Terrace - S10-E2
Continuity mistake: During the very last scene Homer is sitting on the sofa next to Bart watching the news. But in the last shot he's sitting in a separate chair next to the sofa.
Marge vs. Singles, Seniors, Childless Couples and Teens, and Gays - S15-E8
Continuity mistake: In the bathroom, Lisa can't stand the Roofi CD being played so she pulls the plug out of the plug socket to stop the radio playing. In the next shot, the plug has disappeared from the radio. (00:02:15)
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)
I Love Lisa - S4-E15
Continuity mistake: When Homer and Bart are watching a clip of Sideshow Mel on wowee sauce and Bart then says "I'd give anything to go to that show", he has nothing in his hand. The shot cuts to Homer and he then says "I'd sell my first born son" and then the shot cuts back to Bart. When the shot cuts back to Bart, a Buzz cola can has appeared in his hand out of nowhere. (00:08:20)
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
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)
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 robber shoots Apu, he is shot around his leg. In the next shot, the wound is in his chest.
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