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.
The Old Man and the Lisa - S8-E21
Continuity mistake: When Lenny is sitting at Mr Burns' desk, you can see there is nothing in front of him on the table, but in the next shot a "Lenny" name card appears.
The Old Man and the Lisa - S8-E21
Continuity mistake: When Smithers tells Mr Burns that his money has gone, you can see there is nothing on the blue pad on the table, but in the next shot two fountain pen holders have appeared.
The Old Man and the Lisa - S8-E21
Continuity mistake: When Principal Skinner is at the Recycling Centre, you can behind him there are steel drums but in the next shot they have changed to newspapers.
The Old Man and the Lisa - S8-E21
Continuity mistake: When Mr Burns is speaking to his lawyers in his office, there is a blue pad on the table that keeps disappearing and re-appearing between shots.
The Old Man and the Lisa - S8-E21
Continuity mistake: When we see Mr Burns speaking to his lawyers, you can see there is a book stand on the table, but in the next shot it has gone.
Continuity mistake: The doormat at the Blind Man's house is initially coloured blue, but when Bart steps on the squeaky toy, look at the mat and you can see there is now a dark blue border around it.
Continuity mistake: When Bart sees Santa's Little Helper by the window at the Blind Man's house, the window frame is divided into sections but in the next shot it is plain.
Continuity mistake: When Bart goes to push the doorbell on the Blind Man's house, the doorbell is initially on the wall but in the next shot it is on the doorframe.
Continuity mistake: When Willy is speaking to Bart, you can see there is a plate in front of him when he tosses the bone away, but when we see Willy a couple of shots later, the plate has gone.
Continuity mistake: When Moe is talking to the Repo Depot Proprietor, the till on the desk changes position 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