Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: At the start the amount of soap by Burns' head changes drastically and instantly. (00:01:30)
Continuity mistake: The angle of the door at the end changes from partially open to fully open instantly. (00:20:30)
Continuity mistake: When the one member of Aerosmith invites Moe up on stage his guitar simply vanishes. (00:13:40)
Continuity mistake: When Lisa asks for a virgin Moe, Homer's Duff can is missing its colourings. (00:11:10)
Continuity mistake: Lisa asks Homer to go to Dr Hibbert's office, when she does, Homer's hand on the window changes places between shots. Note the vertical bars. (00:15:50)
Other mistake: At the finish line, the crowd are missing all their appearance features such as faces, hair etc. (00:13:50)
Continuity mistake: In the garage Homer rolls up one sleeve but in the next shot both are rolled up. (00:10:35)
Continuity mistake: When McBane's partner asks him to do just one thing for him, the picture keeps appearing and disappearing from his hands. (00:05:30)
Lisa's Pony - S3-E8
Continuity mistake: When Ralph is sat on the fence watching Lisa, his position changes between shots. Note the fence post in relation to his body. (00:15:20)
Lisa's Pony - S3-E8
Continuity mistake: When trying to get a loan, Homer is tapping his fingers on the counter. When the shot changes, his hands are by his side. (00:10:00)
Lisa's Pony - S3-E8
Continuity mistake: When applying for the loan, a bell appears on the counter in front of Homer. (00:10:00)
Continuity mistake: During the Planet of the Apes musical segment, just before Troy McClure sings "Can I play the piano anymore?", he and Dr. Zaius are standing far apart. In the next shot, they are close together.
Kamp Krusty - S4-E1
Continuity mistake: When Lisa gets her report card, the big blue "report card" disappears from the card after she puts it down. (00:04:10)
Continuity mistake: After Phil eats the "horse" egg at Moe's he asks to be taken to the hospital, and when it cuts back to Homer at the power plant, the direction of the stripes on Homer's tie switch to the opposite direction, mid shot. The same thing occurs again later. First, when Homer is standing outside the office while Fred talks to Burns about the benefits package, and also when Homer can't stay for Marge's turkey breakfast. (00:07:05 - 00:12:20)
The Day the Violence Died - S7-E18
Other mistake: At the end of the episode Lisa and Bart watch Itchy and Scratchy in the TV room, which is beside the kitchen at the back of their house. The TV room has a window that faces the backyard, with the record player on a shelf in front of that window. The problem is when Bart looks out the back window and sees Lester skateboarding past the house, the view outside is actually the street in front of the Simpson house, not their backyard as it should be.
Continuity mistake: After John shows up in his car to take the Simpson family for a drive, Marge has her purse strap hanging off her left shoulder when she asks Homer to at least say hello to John. In the next shot, as she tells Homer that he liked John that morning, note Marge's purse strap is missing from her shoulder, but the purse is still there just hanging in midair under her arm. The strap reappears in its proper place in the next shot. (00:07:50)
Continuity mistake: When Marge runs after Bart because he's hiding something under his jacket, Homer pulls out a gate to block Bart's entrance to the TV room. Three different gate styles are shown. (00:20:35)
Revealing mistake: While Homer is waiting for Marge to come downstairs, both Patty and Selma are wearing turtlenecks. When Homer thanks Mr. Bouvier, in the next wide shot as the twins nod their heads, both of their turtlenecks are not colored in properly at their torsos, so the background is visible through their bodies. (00:16:30)
Continuity mistake: At bedtime, while we hear Marge singing to Lisa in her bedroom Bart is lying in his bed, and on Bart's nightstand beside the door there's a framed photo of Krusty and an alarm clock, but in the next closeup the photo has vanished and instead there's a Krusty telephone. (00:15:55)
Continuity mistake: After Brodka lets Bart go with a warning the boy rides his bicycle home, and in the closeup the handlebar's single brake lever is at Bart's right hand, but in the next wide shot the brake lever is at his left hand. In the closeup there's also a bar at the center of the handlebar, but it's gone in the wide shot. (00:09:05)
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