Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: During the breakfast scene, the piece of toast that Homer is holding in his hand disappears.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Homer is eating his toast at the breakfast table, you can see there is nothing on the fridge behind him, but a quick cut to Marge, we return to Homer and a drawing has suddenly appeared.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: In the meeting with Mr Burns and his advisers, one of the advisers holds up a photo of a guy who dated Mary Bailey and the adviser's tie is green. When he is sitting down in the next shot, his tie is now yellow.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Mary Bailey has a group of interviewers around her her tie is blue, but in a close up of Mary in the next shot, her tie is purple.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Mr Burns is doing his TV commercial, the grass in the bowl of the three-eyed fish is light green in some shots, but in close-ups it is dark green.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When the man turns over the picture of Mary Bailey on the flip chart, the words "Artists Conception" are missing.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: During the meeting, Mr Smithers is sitting by Mr Burns and you can see there is nothing in front of him, but when the camera angle changes to behind Mr Burns in the next shot, a glass has suddenly appeared.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When we see the picture of Mary Bailey on the flip chart, the wording "Actual Photo" underneath the picture changes position between shots.
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.
Continuity mistake: At the end of the Capital City number, where the car comes towards camera before they shout "Capital City, yeah", watch Marge's dress. It's green as the car approaches, but as soon as it parks, it turns red, right before your eyes.
Continuity mistake: When Mr Burns and Smithers are standing outside Springfield Stadium, Mr Burns says to Smithers, "Put a little smile on his card" and Smithers is writing it down with a pencil in his left hand. When the Simpsons arrive in the next shot, the pencil has changed into another piece of paper.
Continuity mistake: When Bart says to Homer that he's on "Jumbo-Vision", the man behind Homer is drinking from a paper cup with a straw, but when we see Homer on the screen, the paper cup has disappeared.
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