Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Mr Burns attempts to bribe the Government Inspector in his office, his nameplate is on the door. When Mr Burns shuts the door to leave the Government Inspector alone with the money, his nameplate is gone.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When we see Mr Burns and Mr Smithers in the office at the Springfield Nuclear Power Plant, you can see there is a rectangle on the wall. When the inspection team arrive, the rectangle has gone.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: During the breakfast scene, Homer puts his spoon in front of Maggie's high chair. When he stands up from his chair, the spoon has gone.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: At the start of the breakfast sequence, you can see there is nothing by Homer's bowl, but in the next shot a pink mug appears.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Bart and Lisa are fishing outside Springfield Nuclear Power Plant at the beginning of this episode, you can see there is nothing on the banks behind them. When Dave Shutton approaches them, some rocks have appeared.
Continuity mistake: At the BBQ, Homer lights the grill on fire with a match. When Lisa walks out with the bowl of gazpacho, the fire instantly disappears. (00:13:05)
Audio problem: When the radio is playing "Wannabe", the song stops but Homer doesn't touch the radio.
Strong Arms of the Ma - S14-E9
Audio problem: When the piano is playing Fur Elise, the keys do not move.
Kill the Alligator and Run - S11-E19
Continuity mistake: When The Simpsons are being chased by the police, the cop is seen yelling at Homer. When the shot changes to Homer, the cop pulls out a gun from thin air and shoots.
Simpsons Bible Stories - S10-E18
Continuity mistake: When Bart is trying to wake up Homer, Maggie is seen with a blue pacifier. In the shot after the next, Maggie's pacifier is red.
Other mistake: Marcia Wallace is credited as a special guest voice even though Mrs. Krabappel's role was cut. (00:29:00)
Continuity mistake: When Lisa comes down the stairs prior to watching "When Buildings Collapse", the TV screen is near enough in the corner of the living room and can be seen from the stairs. When Lisa enters the living room, the TV has moved further into the room. Subsequent shots of the TV move it so far into the room that it would not have been possible to see it from the stairs at all in the first place.
The Fabulous Faker Boy - S24-E20
Continuity mistake: When Marge is talking to Bart, in the shot of Marge, there's a tree in the backyard, in another shot of Marge after the one with Bart and Lisa, the tree is gone.
The Old Man and the Lisa - S8-E21
Continuity mistake: When Lisa tears up Mr Burns' cheque at the end of the episode, there is nothing behind her. But in the next shot, a lamp shade suddenly appears.
The Old Man and the Lisa - S8-E21
Continuity mistake: When Mr Burns tries to give Lisa a taste of Slurry at the recycling plant, he has a spoon in his right hand. But when we see Mr Burns a little later on, the spoon has gone.
The Old Man and the Lisa - S8-E21
Continuity mistake: When we see Mr Burns and Lisa during the recycling scene at the Retirement Castle, you can see behind them there are bags containing items for recycling, but in the next shot the bags have gone.
The Old Man and the Lisa - S8-E21
Continuity mistake: When Lisa spots a fish trapped in a can holder on the beach, she takes the fish out of the holder and drops it on the ground. But when Lisa throws the fish into the sea, there is no sign of the can holder.
The Old Man and the Lisa - S8-E21
Continuity mistake: When Mr Burns enters the Simpsons' house, Mr Burns puts his hat on the floor and goes down on his knees and starts praying. But when Lisa is speaking to Mr Burns, the hat has gone.
The Old Man and the Lisa - S8-E21
Continuity mistake: When Grampa Simpson says "That's the activity room" to Mr Burns at the Retirement Home, you can see that Mr Burns and Grampa both have glasses on their trays. In the next shot, Mr Burns' glass is on the table and Grampa's glass has moved from the left to the right.
The Old Man and the Lisa - S8-E21
Continuity mistake: When the two store assistants see Mr Burns looking at the Ketchup and Catsup bottles, the items on the shelves behind them change 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