Continuity mistake: After Homer pushes in front of Lisa in the queue for the bathroom, she loses the toothbrush she was holding in her left hand. (00:01:15)
Continuity mistake: When we first see the medicine cabinet in the Simpson's bathroom the hinges are on the left. When Homer pokes it with the wire it opens as if the hinges are on the other side. The last time we see it, when Lisa rescues Maggie, the door is missing altogether. (00:01:25)
Continuity mistake: After he takes a puppy from Bart, Snake's car appears from nowhere. (00:04:15)
Continuity mistake: When Krusty ends up at his old neighbourhood, the street changes between shots. E.g. the "LLBeanie" sign appears above the door of the 2nd shop and the suit of the man reading the newspaper changes from grey to blue. (00:05:25)
Continuity mistake: When Krusty enters the Jewish Walk of Fame building, there are no stars on the pavement outside it. When he leaves there are. (00:06:15)
Continuity mistake: When Lisa is helpfully explaining what a Bar Mitzvah is, Krusty's new puppy loses its red lead. (00:07:30)
Continuity mistake: While Krusty is describing his prostate to the children, the green umbrella vanishes from beside Lisa. (00:07:40)
Audio problem: When Marge says she wants the padding that goes under rugs her lip movements don't match what she's saying. (00:13:25)
Continuity mistake: When Krusty is sacked, his bottle of pop vanishes. (00:13:45)
Continuity mistake: When Homer writes an autograph for Ralph at the restaurant, Lisa is sitting opposite Marge, has yellow liquid in her glass and has red and brown food on her plate. In the next shot, Lisa is opposite Homer, has a blue drink and has white and green food. (00:14:25)
Continuity mistake: When Homer leaves the studio after being cancelled there is no sign next to the door. When Marge walks up to comfort him there is now a 'stage door' sign there. (00:18:35)
Continuity mistake: During the 'whose garter is this?' joke Patty and Selma appear behind the Simpsons. (00:20:10)
Continuity mistake: In the Itchy and Scratchy cartoon 'A Briss Before Dying', Itchy throws Scratchy's eyes out of the window, but after putting the rest of his body through the grinder the eyes are back.
Continuity mistake: The coathanger is too small to reach the medicine cabinet.
Continuity mistake: After Lisa unlocks the bathroom door with the coat hanger, the puddle of "baby blood" (Pepto-Bismol) at her feet disappears in the next shot.
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