The War of the Simpsons - S2-E20
Continuity mistake: When Homer has caught General Sherman he beats it with an oar so that the oar snaps in two. Then suddenly Homer rows with both oars intact.
Three Men and a Comic Book - S2-E21
Continuity mistake: When Martin is tied to the chair near the end of the episode, the number of ropes tied to him change from four, then to three, and then back to four.
Three Men and a Comic Book - S2-E21
Continuity mistake: When Martin is tied up in the treehouse, at one point Bart takes the brick off the comic book and sets it down near Martin. When Bart and Millhouse fight, the brick disappears.
Three Men and a Comic Book - S2-E21
Continuity mistake: When Bart, Martin and Milhouse start to fight, the Radioactiveman issue 1 that they were protecting has disappeared from the table. Then when Marge brings up some food, they all start eating. The table has disappeared altogether.
Three Men and a Comic Book - S2-E21
Continuity mistake: When there is a rotating shot of Bart, Martin and Milhouse up in the treehouse, the shot never goes past the table, even though it should.
Three Men and a Comic Book - S2-E21
Audio problem: When Homer offers to take the family to Krusty Burger, Lisa is heard cheering, even though her mouth is closed.
Blood Feud - S2-E22
Other mistake: When Moe refills Homer's glass with beer and hands it to him, it briefly disappears and then suddenly reappears. (00:19:01)
Blood Feud - S2-E22
Audio problem: When Homer is kicking the postbox, Barney says something like "Fight the power" but his mouth never moves.
Blood Feud - S2-E22
Continuity mistake: When Mr. Burns gets up after the blood transfusion, Dr. Hibbert is incorrectly colored yellow instead of brown.
Other mistake: There are two mistakes when Bart calls the Krusty Hotline: 1, The cereal box says the phone number is '1-909-O-U-KLOWN.' Bart presses eight buttons on the phone. 2, as he is dialing, you can HEAR seven buttons being pressed. (00:01:45)
Continuity mistake: When Mr. Burns notices that Homer is wearing a pink shirt to work, when he pauses and zooms in the video, Homer is looking almost directly at the camera. In the next shot, though, he is looking more to his left. The people surrounding him also change. (00:03:05)
Continuity mistake: Bart opens the house's front door, then the shot zooms out to show us that all of Springfield is at the Simpson house. In the next shot with Mayor Quimby the door is suddenly closed. (00:15:30)
Audio problem: When Bart says "Krusty Hotline" his mouth doesn't move.
Audio problem: When Homer is in the asylum talking in his sleep, his mouth stays open when he's talking.
Audio problem: When Michael and Bart are playing a song to Lisa, Bart uses her bin as a drum. Sometimes you hear tapping, but Bart doesn't touch the bin.
Continuity mistake: After "Michael" comes out of the Simpsons' car, there's a shot of the crowd's shocked reaction. Oddly, Groundskeeper Willie seems to have grey hair and brown skin.
Mr. Lisa Goes to Washington - S3-E2
Other mistake: The first time we see all three children staring at the TV, the interior of the Simpson house seems different. (00:02:30)
Mr. Lisa Goes to Washington - S3-E2
Audio problem: When Lisa is reading her speech for the essay contest, what she says does not match her mouth movements. (00:06:30)
Mr. Lisa Goes to Washington - S3-E2
Audio problem: When the lady is asking questions to Homer before Lisa wins the trip to Washington, what she says doesn't match her mouth. (00:07:20)
Mr. Lisa Goes to Washington - S3-E2
Continuity mistake: When Lisa approaches the Abe Lincoln statue, there is an old person near her. In the next shot, there are three people suddenly surrounding her. (00:15:05)
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