Continuity mistake: When Santa's Little Helper is taken away by the Repo Men, the van's back bumper is first seen to have no number plate. When the van drives off, there is a number plate.
Continuity mistake: When handing out the mail, Marge places a miniature jerry can of petrol on the table. It is gone in the next shot.
Continuity mistake: In the opening scene of the episode, envelopes are pushed through a mail-slot on The Front door. However, when Laddie arrives and Bart goes outside to meet him, The Front door's mail slot has disappeared.
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.
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.
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