Lisa on Ice - S6-E8
Revealing mistake: After the buzzer goes on the final game and the crowd reacts one of the crowd members says "Tie Game.", then some woman in a red top says "What the Hell.". If you look at the woman when she moves her head you can see the nose on her face disappears. (00:19:55)
Continuity mistake: When Moe gets bitten by the snake in the cash register, he has bites all over his hand. But in the next shot when Barney sets him on fire, all the bite marks are gone.
Springfield Connection - S6-E23
Continuity mistake: When the police pull up outside the station they park three cars in front of the entrance,in front of the steps. In the next shot they are apart on the road, then when Marge walks by them they are in a line to the side of the steps.
Continuity mistake: When Homer is threatening to boot the Prime Minister, he is holding him still with his left arm. When the shot goes to behind Homer, he has his right arm on the Prime Minister's shoulder. When the shot cuts back to a direct view of Homer, his right arm isn't touching the PM.
Tree House of Horror V - S6-E6
Other mistake: At the speed that Homer was chasing the family outside the lodge at the end of "The Shinning", he would have caught them up with ease.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: Homer crashes through the security barrier then skids to a halt on concrete. But, a shot later, the car is on a field which wasn't there before.
Audio problem: When McBain is explaining about his movie on TV, we see a clip from his movie, in which he uses a machine gun. He throws it on the floor but we don't hear a sound of it crashing on the floor.
Continuity mistake: Two guards take down and eat the embassy flag. But when the Simpsons look down at the frogs at the embassy, the flag is still up on the pole.
Continuity mistake: During the "We Do" song, there is a character at the top of the screen who keeps changing colour. I think it might be Dr Hibbert, but his skin colour keeps flickering to yellow.
Continuity mistake: When Bart is trying to get the toilet water to flow the other way, the toilet can't refill that quickly with that number of flushes.
Continuity mistake: When Cletus takes a picture of one of the robots at the parade, the old lady next to him changes from black to white between shots.
Tree House of Horror V - S6-E6
Continuity mistake: In 'Time and Punishment,' in the basement, as soon as Homer puts the back of the toaster back on, two pink wires taped to the side of the toaster suddenly appear. (00:09:30)
Tree House of Horror V - S6-E6
Continuity mistake: When Skinner is cooking the kids, he and the cook are chasing Bart, Lisa, and Milhouse. From the back, he has an apron tied around his neck. In the next shot, he puts on an apron.
Continuity mistake: When Bart is first introduced to the Superfriends, Ham moves around the table a bit. First he is seen sitting next to the kid with dark, curly hair, and you can see a plate in between him and Bart's plate, indicating that someone else is sitting there. This someone turns out to be Lisa, who after she is introduced, switches seats with Ham, making Ham sit next to Bart.
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When Homer is walking upstairs after kicking Patty and Selma out for the second time, the wall that Homer was approaching is a darker colour than it usually is, and Homer walked up the stairs slowly. But a second later he closed a door, indicating that he went into a room. Are we really to believe that he could go very quickly from the stairs to a room in a matter of seconds?
Continuity mistake: Before Bart notices the lemon behind the lemon-shaped rock there is actually no lemon there. We can later see that there is too much of a significant gap between these two objects for the lemon to be hiding behind the rock.
Continuity mistake: Just before Homer (dressed as Krusty) is picked up by Officer Wiggum, his car is brightly painted and has wobbly clown wheels. When he pulls over it's back to the ordinary dented purple car he usually drives.
Homer Badman - S6-E9
Continuity mistake: Just after Marge's left jacket pocket bursts open at the candy convention the shot changes to a shot of Marge's face. The next shot her right pocket has suddenly burst as well and the candy in it is no where to be seen.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: While hiding the fact they are looking at sex books from Bart and Lisa, Homer picks a green book. When we see what he's reading, it's a grey "Maple Thorpe" book.
Homer Badman - S6-E9
Continuity mistake: When one of the pockets of Marge's coat explodes (when Homer is stealing the rare Gummi), a huge pile of candy comes pouring out. When she bends down to pick some up, there isn't nearly as much candy there as before. There are people picking up the candy with her, but they would have to pick it up extremely fast, and they aren't.
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