Continuity mistake: When Krusty the Clown arrives at the beauty pageant his tie is done up. When he goes on stage it is undone.
Continuity mistake: When it is announced that Amber is the winner of the contest, and Lisa is runner-up, the stands in the back of the stage are empty. However, when Lisa walks off, all the contestants are back on the stands. (00:15:00)
Continuity mistake: When Krusty appears on stage he has a microphone that vanishes from his hands when he claps at the end of the song. (00:13:10)
Continuity mistake: When Homer comes into the kitchen to ask what 1 thing Lisa would want most, the milk carton and glass disappears from the table for a few shots. (00:07:10)
Continuity mistake: When Millhouse first spots the spookhouse, there is a red item on the floor by him, as he walks towards the spookhouse the item has gone. (00:03:00)
Continuity mistake: When Lisa says she will do the pageant, her clock goes from 8:05 to 7:55. (00:08:30)
Continuity mistake: When Homer and Marge are talking about Homer seeing Lisa through a fathers eyes, the clock on the wall simply disappears. (00:08:00)
Continuity mistake: The time on the clock when Homer comes into the kitchen keeps jumping forward in massive leaps. (00:07:30)
Revealing mistake: Krusty's nose flashes white for a split second during his song for the winner of the Little Miss Springfield pageant. (00:15:06)
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