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.
Continuity mistake: When Moe is wiping the beer glass at the beginning of the episode, the glass is initially smooth but changes to dimpled in the very next shot.
Continuity mistake: When we first see Homer at Moe's at the beginning of the episode, he is sitting at the bar and there is an ashtray by his glass of beer. But after a quick cut to Moe, we return to Homer and the ashtray has disappeared.
Continuity mistake: Bart is putting pool balls while training with Lisa, the 2 balls remaining on the table change from white to a pink/red. (00:14:20)
Continuity mistake: During the tournament, Abe Lincoln hole, there is only one hole to shoot for when his legs open up, after Todd hits his ball through, you see 3 holes from the backside. After Bart hits his ball the legs open up to reveal 3 holes to shoot for from the frontside. (00:19:25)
Continuity mistake: When the Flanders and Simpsons first meet at the golf course, Flanders is wearing his usual long-sleeved green sweater over his shirt. After Homer says to him, "The fruit of my loins can beat the fruit of your loins any day of the week", the color of Flanders' sleeves is missing, making it look as if he's wearing a sleeveless pullover.
Continuity mistake: When Flanders' wife gives them the sandwiches in the recreation room there are 12 sandwiches, when Homer asks Ned to get him a beer there are only 6.
Continuity mistake: Flanders is seen signing the agreement with his right hand. In later episodes, he is known for being left-handed.
Continuity mistake: When Patty and Selma bring food to the Simpsons' for one shot Patty's dress turns blue before turning purple again.
Continuity mistake: As Milhouse walks up to the TV to turn up the volume, Lewis is nowhere to be seen in a wide shot, but as Milhouse walks back over to the couch you can see Lewis sitting on the floor. (00:02:15)
Continuity mistake: When the family is talking at the dinner table about going to see Truckasaurus, the amount of food on everyone's plate continually changes between shots. (00:03:40 - 00:04:25)
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