Continuity mistake: When Homer starts the song at the end of the episode, the doors to the house behind him are open. In the next shot of the house they are closed, then they are open again in the next shot.
Brother From Another Series - S8-E16
Continuity mistake: When in the dam Bob stops the motors from spinning. Next shot shows the blades spinning again, but when the camera cuts they are stopped again.
Tree House of Horror VII - S8-E1
Continuity mistake: In Citizen Kang, when Homer bursts in at the Dole-Clinton Debate, you can see the wall behind him is light blue, but when we see a close-up of Homer, the wall is now brown.
Brother From Another Series - S8-E16
Continuity mistake: Sideshow Bob and Cecil's glasses keep switching from wine glasses to champagne glasses while they are having dinner.
Continuity mistake: Lenny says that Homer got his job by showing up when the nuclear plant was opened. In the episode "I Married Marge" (Season 4), the plant is already open when Homer interviews for a position, doesn't get it, then works at Gulp 'N' Blow.
Continuity mistake: While Marge and Homer are standing by their front door when everyone leaves the house Marge is wearing earrings, but when it cuts to the closeup both of Marge's earrings have vanished. (00:08:10)
Continuity mistake: After Marge has bitten the candle down to size, when she wipes Bart's face her left earring vanishes. (00:03:35)
Continuity mistake: After John shows up in his car to take the Simpson family for a drive, Marge has her purse strap hanging off her left shoulder when she asks Homer to at least say hello to John. In the next shot, as she tells Homer that he liked John that morning, note Marge's purse strap is missing from her shoulder, but the purse is still there just hanging in midair under her arm. The strap reappears in its proper place in the next shot. (00:07:50)
The Itchy & Scratchy & Poochie Show - S8-E14
Continuity mistake: During the last taping of Homer's Poochie character, June Bellamy is standing beside Homer, and she's wearing a watch on her left wrist, but her watch vanishes in some shots. (00:19:40)
Continuity mistake: When Ned stops to snap at Lisa he's already yelled at Marge and Bart. Yet in the background you can see Marge among the secondary characters.
Simpsoncalifragilisticexpiala(Annoyed Grunt)cious - S8-E13
Continuity mistake: When Bart is lying on his bed whipping cupcakes at the wall, there are already 2 on the wall but after he whips the 3rd, there are still only 2 cupcakes on the wall.
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.
The Old Man and the Lisa - S8-E21
Continuity mistake: When Mr Burns is looking at the Ketchup and Catsup bottles in the supermarket, there is nothing in front of him but in the next shot his trolley appears from nowhere.
The Old Man and the Lisa - S8-E21
Continuity mistake: When Smithers tells Mr Burns to "maintain your dignity", you can see there is a cup, plate and spoon on the table. In the next shot, all three items have 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