Tree House of Horror V - S6-E6
Other mistake: At the end, just before the Simpsons are turned inside-out, Bart is not only wearing his red shirt in bed, but sitting in a position that's not even possible in any position he was sleeping in. (00:20:35)
Continuity mistake: Wiggum asks Homer for another burger and Homer throws it to him. When he catches it Otto has disappeared from sitting next to Eddie.
Much Apu About Nothing - S7-E23
Continuity mistake: In the final high-up shot of the Simpson's garden with everyone chanting 'No on 24'; Lisa has disappeared from next to Apu, and Ned Flanders' glasses have vanished.
The Secret War of Lisa Simpson - S8-E25
Factual error: When Bart smashes all the glass in Springfield(as a result from the sound wave he made by speaking through the mega phones)the car windows get smashed as well. But when we see Chief Wiggum and Homer's car, the glass is still intact.
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: After Maggie makes her wish, the family jumps from being in their seats to beside the window. (00:03:50)
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: When Marge is on the phone to her sisters, her necklace changes from white to red.
Continuity mistake: At the beginning, when we see the exterior shot of the bus, it is full of kids. In the interior shots, 1) before the twins talk to Bart and Milhouse, every seat is empty, even Sherri and Terri's. 2) when the bus arrives at the school, we AGAIN see a full busload of kids. (00:01:30 - 00:02:25)
Audio problem: When Otto says that he was on his way to Mexico, his mouth doesn't move in the interior shot of the bus. (00:04:20)
Continuity mistake: Marge said to Bart she would make Butterscotch chicken for him, but in the Season 2 episode "Blood Feud" Marge says Bart's allergic to butterscotch.
Continuity mistake: When Homer is sitting in the Frying Dutchman with the crowd gathered round looking at him, the Captain invites people in. Some start walking in, but in the next shot where they are all gathered round again, it is the same group of people again. (00:17:00)
Pygmoelian - S11-E16
Continuity mistake: At the start of the episode, Homer wakes the family up and they get in the car in their night clothes. When they arrive at the destination, they are dressed.
Other mistake: When Ned and Homer's raft is going fast, Ned decides to go on the left side of the gorge, so he paddles on the left side, which causes a raft to turn to the right, which 1, means the raft moved to the left, which is impossible, and 2, he wanted to go to the left, but paddled like he wanted the raft to turn right.
Continuity mistake: After Selma gives Madam Wu the sack of ten thousand "happinesses" the sack instantly vanishes from off the table. (00:08:40)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: When Jimbo and Kearney take Homer's candy, it is obviously night time. However if you watch the outside as Homer closes the door before he says "Lousy punks" it shows a daytime sky.
Continuity mistake: After Bart and Milhouse drink the all-syrup squishee, the syrup disappears from Bart's face between shots.
Burns' Heir - S5-E18
Continuity mistake: When Smithers finds Burns drowning in the bathtub, he throws the rag. When the rag hits the floor, it magically disappears.
Continuity mistake: When Homer is taking the kids to school for the second time the view behind him doesn't look further away while driving.
Brake My Wife, Please - S14-E20
Continuity mistake: When Hibbert handcuffs Bart to the radiator, for one brief second, his cast and bandages disappear. They return in the next shot.
Sweets and Sour Marge - S13-E8
Continuity mistake: When Homer falls off the human pyramid, he grabs onto someones rear end to stop himself from falling. In the next shot, he is suddenly holding a foot.
Continuity mistake: When Homer opens the door on Bart the door handle is purple with a grey backing. Later when Homer is saying 'If I went to a BBQ and there's no meat...' there is only the purple knob.
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