Continuity mistake: When Wolfcastle says that 'Jay Sherman insulted him, now he will die', for a few shots the shadows are on the floor before they magically disappear. Also, the shadow of the gun does not match the real gun.
Continuity mistake: When the Simpson family and Jay Sherman are having dinner, things like the food from their plates, their knives and forks and even Homer's burping trophy disappear and then reappear for a couple of seconds before disappearing again.
Audio problem: When McBain is explaining about his movie on TV, we see a clip from his movie, in which he uses a machine gun. He throws it on the floor but we don't hear a sound of it crashing on the floor.
Continuity mistake: When everybody is chanting 'Film Festival', you can see that Mayor Quimby has his arm up. But in the next shot, which changes so that you can see Marge, he his holding up his other arm.
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