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.
Continuity mistake: When Bart arrives at the Repo Depot, he has nothing in his hand, but when he walks through the door, a photograph suddenly appears.
Continuity mistake: When Marge is speaking to Bart at the dinner table, there is a fork by Bart's plate that disappears in the next shot.
Continuity mistake: When Bart and Laddie are at the Springfield Town Hall, you can see there is nothing on the wall behind them, but in the next shot a plaque appears.
Continuity mistake: When Bart is talking to Milhouse in the park, there are two pine trees in the background. When we see the two a little later, the pine trees have gone.
Continuity mistake: When the man in the park throws a Frisbee for Laddie to fetch, the Frisbee can be seen falling to the ground, but when we see Laddie running, the Frisbee is back in the sky again.
Continuity mistake: When Laddie is eating the meat that Bart gave him, Santa's Little Helper's bowl is next to his bowl. When we see Laddie two shots later, there is now only one bowl, and in the shot after that, there are two bowls.
Continuity mistake: When Bart asks his mother if he could feed Laddie during the dinner scene, he has a glass in front of him on the table. But when we see Laddie eating, Bart's glass has gone.
Continuity mistake: Marge is holding a leaflet containing Laddie's instructions when Homer wonders where the dog is, but when Laddie returns, she no longer has the leaflet.
Continuity mistake: When Homer says "Where did he go?" when Laddie wanders off, Marge is standing in front of an archway. In the next shot, she is standing in front of a cabinet.
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.
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