Continuity mistake: In the scene at the United Nations, the Russian placard is just a placard. In the next shot, the placard is attached with a rod to rotate it at the push of a button.
Tree House of Horror VIII - S9-E4
Continuity mistake: Homer is dancing naked in the church and has his pants on the pew. There is then a wide shot and his pants are gone.
Realty Bites - S9-E9
Continuity mistake: The Front door of the Murder House has two windows which vanish, and also a door knob that switches sides so the door opens the opposite way.
Realty Bites - S9-E9
Continuity mistake: Snake has an earring in his right ear, but in some shots the earring is missing then reappears, or it switches to his left ear. Also, when Homer and Snake are fighting on the hood of the car Homer's right shoe falls off, but when the car speeds toward the Murder House, Homer is wearing both of his shoes while he and Snake are still fighting on the hood.
The Trouble With Trillions - S9-E20
Continuity mistake: In the post office when Chief Wiggum is using the megaphone, Otto is seen in the right line as seen from the door but when Kent Brockman attempts to interview him he is magically in the other line, in front of Krusty.
Bart Carny - S9-E12
Continuity mistake: When Cooder comes out of the house to witness Homer throwing the ring onto the chimney, there's a doorbell on the side of the doorway. The next shot, it's disappeared.
Continuity mistake: When Homer is fishing, the colours of the things on his hat switch places between shots.
Continuity mistake: When Frink collapses at the table, his sleeves are green. When it cuts to a wide shot, they are yellow.
Continuity mistake: When Bart and Lisa are in the compound, just before Bart gets brainwashed, the bags that were behind Lisa disappear. Homer and Marge were on the other side of the room, so they couldn't have picked them up.
Bart Carny - S9-E12
Continuity mistake: When Homer is talking through the door to Cooder about getting the house back, the shot is through the fisheye lens on the door and you can see Marge, Bart and Lisa smiling. The very next shot, they suddenly have a frown in no available time.
Continuity mistake: When Lisa comes down the stairs prior to watching "When Buildings Collapse", the TV screen is near enough in the corner of the living room and can be seen from the stairs. When Lisa enters the living room, the TV has moved further into the room. Subsequent shots of the TV move it so far into the room that it would not have been possible to see it from the stairs at all in the first place.
The Trouble With Trillions - S9-E20
Continuity mistake: The To Do Pile doesn't appear until Marge mentions it.
Continuity mistake: When the "Angel" tells everyone to prepare for the end, Carl is seen with yellow skin.
Continuity mistake: While everyone in Springfield is waiting for the apocalypse, Dr. Hibbert's wife Bernice is seen with yellow skin while she's holding on to him.
Continuity mistake: When Dr. Gould says the DNA test was inconclusive, Apu is seen in the background with yellow skin.
Continuity mistake: When Kent Brockman gives his after thought on Lisa's speech, his hair and clothes have changed colors.
Continuity mistake: At one point when Homer is giving his speech in front of the Jebediah Springfield statue, Carl's skin is yellow. In all other shots he is back to his normal color.
Continuity mistake: At one point, while everyone is clapping for Homer during the debate in The Town hall, Apu is seen with yellow skin, and Chief Wiggum is seen with black hair among the townspeople. In all other shots, they're back to their normal skin and hair color.
Continuity mistake: Bart, Lisa and Milhouse run away from the others and are stopped by a cliff. Milhouse then grabs onto a vine which was never there in previous shots. (00:19:00)
Continuity mistake: At the trial, Milhouse moves over to Lisa and Bart is in the middle of them. In the next shot, Bart has disappeared. (00:15:25)
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