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.
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.
Continuity mistake: In the scene where Homer dodges the cannon ball, he is wearing goggles and a helmet. But when Homer jumps down from the platform and hugs Marge, his helmet and goggles have disappeared.
Continuity mistake: Homer opens the door on Bart just before he shows the kids his BBQ invites but there is never a door there in the Simpsons' home, only a doorway.
Continuity mistake: When Marge puts more lamb chops on Lisa's plate they are now grey in colour. Also the ones already on her plate have turned to grey.
Continuity mistake: The moss on Walt Whitman's grave when Homer removes it changes.
Much Apu About Nothing - S7-E23
Continuity mistake: When Willy is threatening the children and Skinner it shows that Lisa has her hands on her sides and she is holding nothing. In the following shots, she has a blue book held against her chest.
Much Apu About Nothing - S7-E23
Continuity mistake: When the mob return to Quimby his assistant's clipboard changes colour between shots.It goes from light brown to burgundy then back to light brown again.
The Simpson's 138th Show Spectacular - S7-E10
Continuity mistake: During the false ending to "Who Shot Mr. Burns: Part 2", Smithers moves position when Burns explains what happened.
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