Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: During the meeting with Mr Burns and his political advisers, there is an adviser in front of the flip chart and you can see it is a blank sheet of paper. But a little later on, the flip chart now has The Front sheet on top.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Homer is on the telephone to Marge at the control panel in the Nuclear Power Plant, the door behind him is closed. In the next shot, it is now open.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Mr Burns sits down on the chair near the desk of his office, there is a brown book on the desk that keeps disappearing and re-appearing between shots.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When the Governor Inspector is in Mr Burns' office, Mr Burns puts money in the pockets of the Inspector's uniform. When the Inspector leaves the office, his pockets are empty.
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.
Blood Feud - S2-E22
Continuity mistake: When Mr. Burns gets up after the blood transfusion, Dr. Hibbert is incorrectly colored yellow instead of brown.
Continuity mistake: When Homer is rolling around on the grass outside the house with Bart, Lisa, Santa's Little Helper and Snowball II after the hair formula works, Snowball II is drastically larger than usual in the overhead shot.
Continuity mistake: When Homer and Karl are selecting a suit, just after Karl says none of the suits are to his liking, Karl's tie changes from green to red.
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