The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: Just before Homer tries biting off the boot, he is wearing a watch. But from then on it disappears off his arm until he is trying to figure out how many hours it is from 9-5.
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: When the camera pans down the Trade Center, there is no washing line there. But a few shots later, a washing line appears.
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: Just before Duff man arrives, Barney has loads of sweat on his shirt. But when Duff man pushes the big jug of beer towards him in the next shot, the sweat is gone.
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: At the very start of the episode, Moe is wearing a watch. But in the next shot when all the guys come in, and all following shots, the watch is gone.
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: In Homer's flashback, when the pimp chases Homer, who is covered in garbage, Homer runs away from him on one side of the street. When Homer runs on the other side of the street, he is not covered with garbage. When he climbs a ladder and falls into a manhole, he is covered with garbage again.
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: During Homer's flashback, Homer passes the sign that says "Jeremiah's Johnson" twice.
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