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.
Continuity mistake: When the Shelbyville kids drop the basket of lemons when Bart and friends start throwing lemons at them, the position of the basket changes when the Shelbyville kids run off. Note the colour of the Springfield grass and the Shelbyville grass.
Continuity mistake: When Marge says good night to Bart he has pyjamas with sleeves on. Then when he puts on Lisa's nightgown (which doesn't have sleeves) to make Marge think he is Lisa, Bart's pyjama sleeves can't be seen under Lisa's nightgown. (00:12:25)
Continuity mistake: During the 20 years ago flashback, when Maude goes to spray water on Homer's pants, she is sitting on a tree in the background. When Homer and Marge talk, she doesn't spray water on his pants, but in the next shot she is gone. (00:17:35)
Tree House of Horror XI - S12-E1
Continuity mistake: In the "Scary Tales can Come True" segment, Bart's plague rat bite disappears for the rest of the segment.
Continuity mistake: During Lisa's and Bart's segment, time seems to run really quickly. When Lisa leaves West Springfield Elementary it is 11:00 and when she gets to Moe's it is noon, then a few minutes later it is 2:50. When Bart and Milhouse find Fat Tony it is noon, then when Bart gets hit by the truck, it is almost 3:00.
Continuity mistake: When Bart goes up to his treehouse to write the kidnap letter, he throws his Murder 4 Life jumper out the treehouse entrance. Later, when Lisa finds the jumper, it is now on a tree branch as if he threw it out of one of the treehouse windows.
Diatribe of a Mad Housewife - S15-E10
Continuity mistake: When Homer goes to Ned to make sure Marge imagines nothing again, Homer puts his hand through the door, then he puts his hand through the mailbox, then Nelson puts his hand out to steal the doormat. Nelson puts his hand just over the mailbox, then in the next shot when it reveals Nelson is there, his hand is suddenly under the mailbox without enough time to move it.
Sideshow Bob's Last Gleaming - S7-E9
Continuity mistake: When Homer drives under the plane to save Bart from Sideshow Bob, you can see he drives under the plane twice.
Thirty Minutes Over Tokyo - S10-E23
Continuity mistake: When Lisa gets the tickets on the "volcano", she is a few inches away from the end of the bridge. When it falls and Marge runs onto the bridge, she is now in the middle of it.
Continuity mistake: When everyone is running out the cave after finding the boar, Wendell's skin is yellow instead of his usual pale white. (00:19:50)
Continuity mistake: When Bart, Lisa and Milhouse are running away from the others, the order is Bart, then Lisa, then Milhouse. In the next shot it is Lisa, then Bart, then Milhouse. (00:18:45)
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