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)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: Burns says he needs to get his plant back. When he does the door behind him is open or closed depending on the shot. (00:19:00)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: When Homer can't sleep, if you look out the window you can see a house in the distance. When the shot changes this house should be visible but it isn't. (00:11:20)
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)
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)
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: In the garage Homer rolls up one sleeve but in the next shot both are rolled up. (00:10:35)
Continuity mistake: When Lisa asks for a virgin Moe, Homer's Duff can is missing its colourings. (00:11:10)
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.
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)
Continuity mistake: While Homer, Carl, and Lenny are at Moe's with their new bud Fred, in the interior shots the swinging front door to Moe's swings open on the left side, but in the exterior shot when they all leave Moe's, that door still swings open on the left side, opposite to the interior shots. (00:08:00)
Once Upon a Time in Springfield - S21-E10
Continuity mistake: Mr. Burns shows a box of doughnuts coloured pink, brown and light brown. When the guys grab them they're all pink.
Continuity mistake: While Marge and Homer are standing by their front door when everyone leaves the house Marge is wearing earrings, but when it cuts to the closeup both of Marge's earrings have vanished. (00:08:10)
Continuity mistake: After Marge has bitten the candle down to size, when she wipes Bart's face her left earring vanishes, then it reappears. (00:03:35)
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)
The Itchy & Scratchy & Poochie Show - S8-E14
Continuity mistake: During the last taping of Homer's Poochie character, June Bellamy is standing beside Homer, and she's wearing a watch on her left wrist, but her watch vanishes in some shots. (00:19:40)
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