Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When Bart tries to buy a ticket to Itchy and Scratchy, the booth is unoccupied. When the shot changes the man has appeared in the booth. (00:19:20)
Tree House of Horror III: The Simpson's Halloween Special III - S4-E5
Continuity mistake: When Bart gets the Krusty doll, he pulls the pull string from the back of the doll. When the doll has finished talking, the pull ring has disappeared. (00:04:05)
Continuity mistake: When Krusty appears on stage he has a microphone that vanishes from his hands when he claps at the end of the song. (00:13:10)
Continuity mistake: When Homer comes into the kitchen to ask what 1 thing Lisa would want most, the milk carton and glass disappears from the table for a few shots. (00:07:10)
Continuity mistake: When Millhouse first spots the spookhouse, there is a red item on the floor by him, as he walks towards the spookhouse the item has gone. (00:03:00)
Continuity mistake: Homer says he wasn't sure if he was doing the right thing in regards to giving up doing to church. When he does he puts his fork down across his knife. When the camera cuts the two utensils are no longer crossed. (00:10:40)
A Streetcar Named Marge - S4-E2
Continuity mistake: When Maggie is looking down at the desk to see the keys, there is a book on the desk as well. When she's looking down at the adult walking into the room the book has gone. (00:14:00)
A Streetcar Named Marge - S4-E2
Continuity mistake: Just as Marge heads out for her 1st audition, the kids go from lying on the sofa to sat up instantly. (00:03:35)
A Streetcar Named Marge - S4-E2
Continuity mistake: When Homer picks up the snacks from the vending machine, 2 items are left on the floor. When Marge is practising her lines a few shots later, the items have disappeared. (00:11:10)
A Streetcar Named Marge - S4-E2
Continuity mistake: When Marge walks across the living room she has a bag in her hand which disappears when the camera changes. (00:03:35)
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)
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