Revealing mistake: When Homer is giving Marge, Lisa and Bart money, Homer puts his hand on Bart's shoulder and whispers 'Mel's movie really stinks'. When he lets go of Bart to say this, he leaves his fingers on Bart's shoulder, but he still has fingers on his hand.
Other mistake: When the Simpsons' drives the electaurus off the edge of the harbour, it is shown that The Front of the car goes downwards. When it cuts to the interior view with the Simpsons' screaming, the view from the back window is tilting down, suggesting the rear is going down and The Front coming up. But in the next shot the car is seen in the water with The Front down.
Continuity mistake: The "dummy" in the episode changes consistently from a real character to a dummy sometimes. When Mel jumps into the vehicle in the museum the "dummy" moves aside. When Mel shoves it out of the way, it stays in one rigid position as if it is a dummy. During the chase, the "dummy" falls on the car behind and its facial expression changes. But when one of the guys from THAT car (not the one Mel was in) goes to the dummy, its head is ripped off and you can see that it is stuffed.
Continuity mistake: The text on the billboard which says "She's having a baby...again!" is black when Mel Gibson and Homer crash through it. After they have landed on the ground, the text on the billboard is white.
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