Continuity mistake: When Bart is writing the card for Milhouse, he is writing on the right hand side of the card. This changes to the left hand side in the close up. (00:01:10)
Continuity mistake: When playing Monopoly the fold in the board is level with the P. Camera changes now the fold is before the O. (00:16:10)
Continuity mistake: Maggie spits a hotel out on to the board which disappears a few seconds later. (00:16:15)
Continuity mistake: When Burns hangs up the phone to Kent Brockman, his name tag on his radiation suit disappears. (00:10:20)
Continuity mistake: When the purple jam pops on the core temperature dial, it leaves some residue on the dial which has disappeared in the very next shot. (00:05:10)
Continuity mistake: When Homer is talking to Lenny and Carl about the movie his pink doughnut disappears from his hand. (00:03:45)
Continuity mistake: The colour of Bart's plate at the BBQ changes between shots. It goes from dark blue to light blue. (00:07:40)
Continuity mistake: When Homer and Ned are talking after Homer tries to return the BBQ, the BBQ moves place on the lawn. Note the stepping stones. (00:17:40)
Continuity mistake: At the end Todd's shirt changes from white to red. (00:21:15)
Continuity mistake: When we see Maude ringing items up on the cash register, it has no external display. When Ned is ringing items up there is an external display. (00:20:45)
Continuity mistake: When Ned and Homer walk away from Ned's car, they are by the flower beds. Camera cuts and they are back by the car. (00:18:00)
Continuity mistake: When Bart taunts Homer, he has nothing on his plate apart from his burger. When Homer runs over a second later there is more stuff on his plate. (00:03:30)
Continuity mistake: When Homer is smelling the BBQ the smoke that's in front of him vanishes instantly. (00:03:30)
Continuity mistake: When Homer is hanging out of the window there is a blue curtain tie visible however this disappears in the long shot. (00:03:30)
Continuity mistake: When Homer is on the sofa, the cushion under his head disappears when he wakes up. (00:03:00)
Continuity mistake: When the paper falls on Skinner there are blue and white tiles in the doorway, when he is hanging from the hoover, the floor is completely blue. (00:19:20)
Continuity mistake: The paper that Bart draws Skinner on changes from ruled to plain. (00:14:00)
Continuity mistake: When Bart draws Skinner before he is declared missing, the paper is flat on the desk in the first shot and held upright in the next. (00:14:05)
Continuity mistake: After Itchy and Scratchy we see Bart and the mob sat in the bar, the mobster at the end of the bar has his drink in 1 hand or 2 hands depending on the shot. (00:08:16)
Continuity mistake: Bart clears some dust off the picture of the Manhattan, once he's made the drink a few seconds later all the dust has gone. (00:06:40)
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