Continuity mistake: The canister the hippies use to destroy the germs in Burns lab has the words "antibiotics" appear after the clock rings.
Continuity mistake: When Lisa is with Apu, Paul and Linda the wall behind her is purple.On a close up of her when she's listening to Apu it's blue.In the next shot it's purple again.
Continuity mistake: During the lamb vision at dinner Lisa is holding her knife and fork. In the very next shot they're on the table.
Continuity mistake: When Marge is cleaning the dishes on the morning after Bart reveals Lisa as a nerd, Marge is seen in close-up with a white necklace. In next shot of Bart and Lisa, as well as the rest of the scene, Marge has a red necklace.
Sideshow Bob's Last Gleaming - S7-E9
Continuity mistake: When Bart and Lisa first enter the Duff Blimp, Bart doesn't have his back-pack on. However, he is suddenly wearing it after the bomb has gone off.
Much Apu About Nothing - S7-E23
Continuity mistake: Homer comes to the Kwik-E-Mart with the new 'American Apu' and sees him reading a magazine. When Apu walks over to Homer, his magazine disappears.
Tree House of Horror VI - S7-E6
Continuity mistake: When the advertisement of Kent Brockman comes to life he is a thin cut out from a bill board, however the next time you see him he is in the shape of Kent Brockman and no longer thin.
Much Apu About Nothing - S7-E23
Continuity mistake: In the early scene where the Simpsons are gathered around the table to eat, you can see that they are eating slices of pie. However, on some of the long shots, the food on their plates changes and looks more like mashed potato and vegetables. Also, in the same scene, in one shot of Lisa, you can see Bart's hand over her plate, but when the angle changes, it is behind her plate.
Audio problem: When Lisa visits Homer at the plant, they are playing astronauts with the radiation suits. When they spin around and around, Homer is laughing but his mouth stays the same.
Continuity mistake: As Bart is forced to show Marge the item (picture frame) he is hiding, he pulls it out of his jacket and he hands it to Marge. As he pulls it out you can see there is nothing in the frame or on the border of the picture frame. After Marge's reaction to the photo we see a close up of the frame and there is now a picture in the frame and some colorful decorations around the frame. Whilst the frame could have been the backside when he pulled it out he never turned it over when handing it to her, and Marge never turned it around when looking at it.
Tree House of Horror VI - S7-E6
Continuity mistake: During the 'Nightmare on Evergreen Terrace' segment, when Bart is running from Willie, he plans to sink Willie in the sandbox. In the first view of the sandbox it is isolated on a field, yet when Willie is sinking in the sand there is a jungle-gym beside the sandbox. (00:11:35)
Continuity mistake: Wiggum asks Homer for another burger and Homer throws it to him. When he catches it Otto has disappeared from sitting next to Eddie.
Much Apu About Nothing - S7-E23
Continuity mistake: In the final high-up shot of the Simpson's garden with everyone chanting 'No on 24'; Lisa has disappeared from next to Apu, and Ned Flanders' glasses have vanished.
Continuity mistake: When Homer is taking the kids to school for the second time the view behind him doesn't look further away while driving.
Continuity mistake: When Homer opens the door on Bart the door handle is purple with a grey backing. Later when Homer is saying 'If I went to a BBQ and there's no meat...' there is only the purple knob.
Continuity mistake: When Marge talks to cable guy, the trees and hammock disappear.
Continuity mistake: In class, when Lisa is sitting at her desk, pondering the Jebadiah mystery, her tray of cookies and glass of milk is very visible. Then when Lisa says "The missing piece of the puzzle. I've got it." and runs out of class, the cookies and milk are no longer there.
Continuity mistake: In the scene where Homer is on stage in Springfield, he's wearing shorts. When he jumps off the stage after dodging the cannon ball, he's wearing pants.
Continuity mistake: In the scene where Selma and Troy McLure get caught by the press outside the resturant, Selma and Troy swap places between shots.
Continuity mistake: When Bart is looking for candy in the cupboards, the wine bottles in the nearby rack change position between shots.
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