Continuity mistake: The lettering on Smithers' desk name plate changes between shots. While he is taking the call from Mr Burns' mother you can see his name "W. Smithers" in black letters. The shot after seeing Burns, who keeps falling asleep, the letters are now red.
Continuity mistake: When Bart visits the kid's train ride, the first shot of it shows that it starts with a big curve before the tunnel. When he goes on it the track is straight before the tunnel.
Continuity mistake: When we first see Homer feeding the can to the goat the background shows a wooden coop. In the next shot, a purple tree stump appears there too.
Continuity mistake: Bart flicks through his chequebook in the car and finishes on The Front page of it having gone through all the cheques. When the shot changes he is holding it open.
Much Apu About Nothing - S7-E23
Continuity mistake: When the mob come to Quimby's office for the first time, the items on his desk change colour and position.
Continuity mistake: When Lisa is first seen petting the baby lamb, she is next to the fence with hay beside her. In the next shot, she's far away from the fence and there's no hay anywhere.
Continuity mistake: After Homer prepares the BBQ he holds out the steak and holds it back in as Lisa speaks. When the shot changes he's holding it out again, and the pile of meat behind him is smaller and has moved slightly under the window.
Continuity mistake: During dinner Marge has no glass to her right. When she says 'Why thank you Homie' a glass has appeared next to her.
Continuity mistake: Throughout the dinner scene, whenever Homer wants the syrup, it disappears and re-appears next to Lisa.
Much Apu About Nothing - S7-E23
Plot hole: At the end Apu finds out he's been chosen for jury duty for the first time. However, in 'The Boy Who Knew Too Much' he was on the jury.
Continuity mistake: Lisa places her Gaspacho on the house end of the table but in a following shot it's at the other end when the dog is drinking it.
Tree House of Horror VI - S7-E6
Continuity mistake: In the 'Nightmare on Evergreen Terrace' segment, in Bart's dream you see a shadow of what looks like someone with four knife-fingers. Then when we see who it is, it is Willie holding a rake. But the rake has five tines, not four, so the shadow is wrong. (00:07:00)
Much Apu About Nothing - S7-E23
Continuity mistake: Willy jumps in and shakes his fists at the children and Skinner who are in a circle around him. Uta has now disappeared from the circle and cannot be seen anywhere when he was there just seconds before.
Much Apu About Nothing - S7-E23
Continuity mistake: When Kearney buys the beer, the shot of the ice cream sandwiches melting in his arm pits shows that the 'Duff' writing on the crate of beer is thinner than previously seen.
Tree House of Horror VI - S7-E6
Continuity mistake: In the 'Nightmare on Evergreen Terrace' segment, in Martin's dream, Willie emerges from the blackboard with a rake which has a wooden handle. When the shot changes the rake handle has changed to being metal. (00:08:25)
Continuity mistake: When Skinner is addressing the class before the meat video we first see him with black trays on the desk to the far right. In the next shot they're much closer to him.
Continuity mistake: After the "sponge incident," Bart is standing in the drive with the sponge packet in his hand. In the next shot he says "everything about me must go," but the packet has vanished from his hand.
Continuity mistake: When Lisa knocks Bart's chop out his mouth she knocks it out front, however, the chop ends up going to the far right and into Homer's mouth.
Sideshow Bob's Last Gleaming - S7-E9
Continuity mistake: When Maggie (sitting on Marge) appears on "Tyrano-Vision," Homer waves his hand in front of her. However, we can see that he isn't leaning over too far, and in the next shot it is clear that both Bart and Lisa are sitting between Homer and Marge, so there is no way he could have reached over to her in the first place.
Much Apu About Nothing - S7-E23
Continuity mistake: When they are locating 'Springfield' on the map the coffee jug on the table is about 1/4 full.In the last shot of Apu the coffee has risen to about 3/4 full.
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