Tree House of Horror V - S6-E6
Continuity mistake: When the Simpsons shed their skin at the end, the skin falls to the floor. In the next shot it's gone.
Tree House of Horror V - S6-E6
Continuity mistake: In the third story, the five remaining students are all in one classroom - Bart, Lisa, Milhouse, Wendell, and Ralph. Ralph disappears when the other four try to escape.
Continuity mistake: As Homer is giving his speech to the dressed up monkeys, all of the monkeys are dressed in blue suits and you can also see there is one monkey next to the stairs on the stage. In the next shot of Homer leaving the stage there is now six monkeys, with only one wearing a suit and it is grey. (00:19:45)
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: Principal Skinner picks up the hamster and throws it away. But his hands are clean as a whistle even though all the hamster was covered with oil.
Springfield Connection - S6-E23
Continuity mistake: When Hans Moleman and Rev. Lovejoy are in the prison they are sitting to the far right of the bench (which is nearest to Homer's cell). Then in the next shot they are to the far left.
Springfield Connection - S6-E23
Continuity mistake: In the police station the blue light on the ceiling disappears from when the police are seen laughing at Marge.
Continuity mistake: When wedding has been just called off, Lunch Lady Doris calls everyone for wedding cake, and among people who rush to it we can see Moe (you can recognize him by his eyepatch), then, Lisa starts to walk off and among the people she passes by you can see both Lunch Lady Doris and Moe.
Continuity mistake: When Homer is kicked out of Moe's the window behind Homer suddenly opens so Moe can throw the record out.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: In this episode, Mr Burns and Smithers are on the balcony of Burns' office. Mr Burns says "It will be like taking candy from a baby. Hey, that sounds like a laugh. Let's try it right now." We see Smithers, whose expression doesn't change as the two go back into Burn's office. In 'Who Shot Mr Burns Part 2', Smithers remembers this event, except now he looks quite shocked when Burns mentions about taking the candy.
Springfield Connection - S6-E23
Continuity mistake: When Marge walks into the hair salon, she is carrying a white bag. But in the next shot when she talks to Mrs Krabappel, the bag is gone.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: During The Town meeting scene, the position of Latin jazz great Tito Puente hops all over the room - he is frequently appearing in the background, but from various angles.
Springfield Connection - S6-E23
Continuity mistake: When Marge sees Homer's car parked illegally over 3 handicapped spots you can see a car parked near Homer's that is orange. Later in the scene when Marge starts writing a ticket up for Homer the car next to Homer's is now a dark brown. (00:14:35 - 00:15:05)
Tree House of Horror V - S6-E6
Continuity mistake: In 'Nightmare Cafeteria,' in the opening shot we see Bart standing on a desk in the back row. It cuts to a closeup, and he is now on a desk in the second row from the back, as well as people appearing around him, such as Milhouse, who wasn't even in the classroom in the opening shot. (00:15:25)
Tree House of Horror V - S6-E6
Continuity mistake: In 'Nightmare Cafeteria,' when Lunchlady Doris spills food on Jimbo, it only goes onto him. In the next shot it is also all over the table. (00:16:15)
Plot hole: In the scene where Bart has to choose the right Roman numeral door in order to avoid the tigers; right as the Shelbyville kids come bursting through the outer door, Bart picks the right door through humorous deduction and escapes. However, the Shelbyville kids are unable to open the door which doesn't make sense, since there is no lock on the door and there wasn't any mention of Bart blocking or sabotaging the door because only a few seconds later we see him on the street continuing to fret about the lemon tree.
Continuity mistake: When Homer starts walking away with the stone of shame, you can see he has no birth mark on him. yet in the next shot all off the stonecutters see the birthmark.
Continuity mistake: At the end of the episode, when we see a wide shot of everyone going to join Ned on the hill (and singing the song) look to the far left. You will see Apu - and his skin is yellow.
And Maggie Makes Three - S6-E13
Continuity mistake: When Homer is trying to get Ned another woman in a different episode, he tells him that there was some footage of Maggie being born that he couldn't get rid of on the tape but in the scene (in this episode)when Maggie is being born there are no video cameras in sight.
Tree House of Horror V - S6-E6
Continuity mistake: In 'Nightmare Cafeteria,' Lisa and Bart run into the basement, to tell Marge they are cooking kids at school. Between shots Bart and Lisa swap places. (00:18:15)
Springfield Connection - S6-E23
Continuity mistake: When Marge is doing her grocery shopping, the boxes of caviar behind her change from green to red.
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