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: 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)
Bart's Friend Falls in Love - S3-E23
Continuity mistake: When Bart admits to Milhouse that he narked on him and Samantha he is facing the bed. When the camera changes, he has turned 90° and is no longer looking at the bed. (00:19:00)
Bart's Friend Falls in Love - S3-E23
Continuity mistake: When Millhouse asks Samantha if he can walk her home, his glasses are well above his ear. As the camera changes his glasses are now lower. (00:07:20)
Continuity mistake: Selma says she wants a separation while leaning forward with her arms behind her. Camera changes and she is stood with her arms closed. (00:18:40)
Continuity mistake: When Selma tells Bob not to worry about the cost of the wedding she has a cigarette in her hand which disappears almost instantly when she grabs Bob's hand. (00:10:40)
Continuity mistake: When Bob is telling his story about picking up rubbish on the side of the road, we see Bob in The Front of a line of people. When we see the convicts in the reflection of the trooper's sunglasses there is someone in front of him. (00:03:20)
Continuity mistake: When Lurleen is in the studio with the Simpson family, Homer has his arms crossed. When Bart asks to do a solo his hands are now in his pockets. (00:14:50)
Continuity mistake: As people throw stuff at the redneck bar, the guy who introduces Lurleen is leaning to his left then instantly to his right between instant cuts. (00:06:10)
Continuity mistake: When watching the draw, the family have their TV dinners on their lap, which seem to instantly disappear between shots. (00:05:10)
Continuity mistake: The way the chapstick is held out for Bob in prison changes from one shot to the next. (00:04:40)
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