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)
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.
Continuity mistake: The location of the comet in the sky changes direction at several points. Whilst it's apparent size and altitude will of course change, the direction it is coming from cannot. As an example, it is seen looming over the power plant towers, but when Ned is on the hill, it's no longer there.
Continuity mistake: When Mr. Burns pushes the child on the swings, he somehow manages to defy the laws of physics. When he pushes the child forward for the last time, he swings forward, then back, hitting Mr. Burns in the head. He then swings forward again, hitting Mr. Burns from behind. Mr Burns starts saying "You've won this round..." and the child then hits Mr. Burns from behind again. In order for this to happen, he would have to go completely around between the second and third hits and you clearly see he doesn't.
Springfield Connection - S6-E23
Continuity mistake: When Marge is in the supermarket, she only has about 4 items in the trolley. But just before the trolley crashes into the cheese model, it is full.
Continuity mistake: When everybody is chanting 'Film Festival', you can see that Mayor Quimby has his arm up. But in the next shot, which changes so that you can see Marge, he his holding up his other arm.
Lisa's Rival - S6-E2
Continuity mistake: When Nelson does his "Grapes of Wrath" demonstration, it splatters all over Skinner's jacket. When he walks over to the rest of the dioramas his jacket is clean again.
Homer Badman - S6-E9
Continuity mistake: When Homer mixes the Pop Rox with the soda he leaves the Pop Rox packaging over the can. After he throws the can and we see it in the air the Pop Rox packaging has disappeared.
Continuity mistake: When Milhouse is spying with his binoculars with an camouflage outfit on, the colours of some patches change in some other shots. E.g The bottom left corner (from behind) changes from dark green to light green.
Springfield Connection - S6-E23
Continuity mistake: Before Marge sees Homer parking violation, if you look at where he is parked over the first handicapped spot there is a car parked in the first non-handicapped spot. A bit before Marge arrests him there is now a non-handicapped spot between the car and Homer's car. (00:14:35 - 00:15:05)
Homer Badman - S6-E9
Continuity mistake: After Marge's left pocket rips in the candy convention, she goes to start picking up the candy when we see that the right pocket has ripped all of a sudden. When Homer and Marge start running away the pockets are no longer ripped and full of candy again.
Springfield Connection - S6-E23
Continuity mistake: When Marge is shopping, there is a blue baby seat in her trolley. In a following shot of her running with the trolley and it going into the cheese display, the seat has gone.
Continuity mistake: When Bart is talking to Jessica after she stole the collection plate money, she is far away from Bart. But when Bart says "but you're not very nice", she is right next to him.
Two Dozen and One Greyhounds - S6-E20
Continuity mistake: When they are in Mr Burns' laundry room, it is shown that Bart wasn't wearing his socks. However, part way through this scene, Bart is wearing his shoes and socks again without having time to put them on.
Homer vs. Patty and Selma - S6-E17
Continuity mistake: At the beginning of the episode, there is a drunk wearing glasses. He disappears in the next shot onwards.
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