The Trouble With Trillions - S9-E20
Continuity mistake: In the scene where Homer is eating a hot dog just before the post office closes for the day, the vendor behind the hot dog cart has a apron over his shirt. The very next shot the apron has disappeared. (00:05:05)
The Trouble With Trillions - S9-E20
Continuity mistake: When Homer is watching TV early in the episode, he has a watch on his left wrist. When he begins working on filling out his tax forms, the watch has disappeared. When he takes down the sailboat painting from the wall, the watch has returned.
The Trouble With Trillions - S9-E20
Continuity mistake: When the FBI agents arrest Mr. Burns he is handcuffed; however, when Mr Burns is being dragged off there are no handcuffs on his wrists at all.
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.
The Trouble With Trillions - S9-E20
Continuity mistake: The To Do Pile doesn't appear until Marge mentions it.
The Trouble With Trillions - S9-E20
Continuity mistake: In the scene where the FBI agent and Homer are going into the photo booth to view the video, look to the right of the photo booth before they enter. There is a white cup next to the booth. After they have watched the video and are standing outside the booth talking, the cup is now red instead of 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