Continuity mistake: There is a latch on the crate when Bart opens it and Laddie appears, but when Laddie jumps out of the crate, the latch has gone.
Continuity mistake: When Bart opens the door and finds the crate containing Laddie, there is nothing on the doorstep but in the next shot a green mat appears.
Continuity mistake: When Lisa comes into Bart's bedroom, the number of balls in the bottom tray of the bagatelle game increase between shots.
Continuity mistake: When Bart sees "The Covet House" order in the catalogue he has picked up from the trash can, he is reading it with both pages open, but when we see him in the next shot, he is reading the catalogue with the back pages folded under.
Continuity mistake: When Bart is at the Card Shop, he picks up the magazine "Zoidzilla" and put on the top of the pile he is holding. But when he takes the pile to the cash desk, The Front cover of the magazine is now coloured green.
Continuity mistake: When Marge discovers a letter for "Santos L. Halper", Bart has nothing in front of him on the table. In the next shot, a knife, fork, bowl and glass have appeared.
Continuity mistake: When we see Bart holding the post, he is initially holding it with one hand, but when we see a close-up of the post in the next shot, he is holding it with both hands.
Continuity mistake: When Marge finds Lisa's German verb wheel in the post during the breakfast scene at the start of the episode, you can see Lisa has nothing in front of her. In the next shot, a bowl and a glass have appeared.
The Old Man and the Lisa - S8-E21
Continuity mistake: Right at the start when Lisa says "I could still use more paper," the plastic can-rings she was holding vanish in the next shot.
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.
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