Burns' Heir - S5-E18
Continuity mistake: When Mr. Burns is sitting in front of the fireplace, he has his normal blue outfit when seen from behind, and a purple night gown when seen from The Front. (00:02:50)
Burns' Heir - S5-E18
Continuity mistake: When Homer and Marge are talking to Chief Wiggum, the Rubik's Cube and the cup on his desk changes to a doughnut between shots. (00:13:20)
Burns' Heir - S5-E18
Continuity mistake: When Homer says, "You idiot," to the programmer, the red ashtray changes position on the desk. (00:15:55)
Burns' Heir - S5-E18
Continuity mistake: The doughnut Homer later picks up isn't by the door when Lenny walks into Mr Burns' office, and we never see anyone put it there.
Burns' Heir - S5-E18
Continuity mistake: Hans Moleman has brown skin at the beginning of the episode and yellow skin at the end.
Burns' Heir - S5-E18
Continuity mistake: A criss-cross pattern appears on the fireplace during the closeup on Smithers after Mr. Burns told him that he doesn't have a heir.
Burns' Heir - S5-E18
Continuity mistake: When Smithers finds Burns drowning in the bathtub, he throws the rag. When the rag hits the floor, it magically disappears.
Burns' Heir - S5-E18
Continuity mistake: Burns' top hat disappears from the bath at the start.
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