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)
Revealing mistake: When the car arrives at the NFI, the car goes straight through the barrier. (00:09:20)
Other mistake: Right before Homer and Bart head to the concert, Homer has the high-pitched ringing in his ears while Marge is talking. Then just as Homer says, "I hear you. C'mon, boy," note Selma's and Patty's skin over their scoop necklines are not colored in properly, it's the same color as their dresses. (00:01:45)
Continuity mistake: In some shots Otto's beaded bracelet vanishes and reappears, such as when he's on the school bus before the accident. Also, note a watch suddenly appears on his left wrist then it disappears, on the school bus. (00:11:05 - 00:15:15)
Continuity mistake: While Otto plays the guitar at 3:00 AM, the tuning keys on the guitar head are first facing down, then the guitar head flips and the tuning keys are facing up, between shots. (00:15:45)
Continuity mistake: When Homer is wearing underwear while banging on the bathroom door the doorknob is missing, but next shot it appears on the door, and the closet door hinge also vanishes. (00:18:25)
Continuity mistake: When Otto's guitar playing wakes Marge and Homer they go to the garage. Note the direction of the door when Homer opens it toward the right, but when Marge asks Bart what's going on, the door's open the opposite way toward the left. (00:15:55)
Brother Can You Spare Two Dimes? - S3-E24
Continuity mistake: When Homer says he doesn't know what the one light switch does he flips it and it shows a merry Christmas message on his roof. However, in subsequent shots, there are no lights attached to the roof. (00:12:50)
Brother Can You Spare Two Dimes? - S3-E24
Continuity mistake: When Herb mentions about "new coke" the homeless man who makes a comment looks like no-one in the group Herb is talking to. (00:03:50)
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