Springfield Connection - S6-E23
Continuity mistake: When Homer first spots Snake dealing, you see Marge with a handbag. In the next shot, the handbag has disappeared.
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When Marge says, "I wish you wouldn't put Homer down like that.", Patty and Selma's dresses swap colour between shots.
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When one of Marge's sisters says, "He blew all your savings on jack o'lanterns.", one of the armrests on the sofa is black for some reason.
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When Homer for the second time throws out Patty and Selma, the knocker just stays in the same place as if the door hasn't opened at all. (It looks like it is floating in mid-air).
Lisa on Ice - S6-E8
Continuity mistake: When Lisa throws her academic alert into the trash, she jumps half way across the stage without taking a step.
Springfield Connection - S6-E23
Continuity mistake: When Marge is making celery soup, The Front view of her shows just the chopping board in front of her. Then when Lisa talks to her the microwave is seen in front of her.
Springfield Connection - S6-E23
Continuity mistake: When Marge is reading the books on death sports the police arrive and she turns around, you can see the two posts with the round balls on top with no words on it. But when Marge starts walking towards the police station it says "Police" on the balls and the post changes size. Also the door to the police station changes from brown to blue to clear glass and back to blue during the scene.
Tree House of Horror V - S6-E6
Continuity mistake: In 'Time and Punishment,' when Homer exits the basement, he discovers Bart and Lisa are giants, and he then screams and runs back to the "basement" - however the same door that leads to the basement seconds ago, now leads to a green -carpeted room, and the basement seems to have vanished. The door is also hinged on the wrong side. (00:12:50)
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When Homer tries to tell Marge how he did in the test, Selma and Patty are holding their cigarettes. In the next shot, the cigarettes are in their mouths.
Continuity mistake: When the Simpson family and Jay Sherman are having dinner, things like the food from their plates, their knives and forks and even Homer's burping trophy disappear and then reappear for a couple of seconds before disappearing again.
Tree House of Horror V - S6-E6
Continuity mistake: In 'Time and Punishment,' Homer goes back in time, then returns, and the kitchen table has plates of food, cutlery and glasses all set out. Then when Homer is informed that Ned is the Lord of the Universe, the house starts shaking, but you can see the table is now totally clear. (00:11:15)
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.
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.
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)
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