Continuity mistake: Throughout the episode, God has 5 fingers. At the end, Homer asks what the meaning of life is, and God has only 4 fingers now. (00:21:20)
Continuity mistake: When talking to the family about no longer attending church, Bart moves behind Homer in an instant cut. (00:07:45)
Continuity mistake: Homer says he's had the best day by not going to church. When he does, Marge has Maggie in her arms. When the camera changes to behind, you can see she no longer is holding Maggie. (00:07:45)
Continuity mistake: Homer asks the family how church was. When he does, Marge grabs her nose. Camera cuts and she is no longer holding her nose. (00:07:30)
Continuity mistake: When Homer spots the penny, he moves his foot and there is nothing on the floor. When the shot changes, the penny has appeared. (00:06:50)
A Streetcar Named Marge - S4-E2
Continuity mistake: Otto's tattoo changes from the close up and the long shot of him when auditioning for Stanley. Note the eyeballs. In the first shot they are past the top hat. In the following they are much further back. (00:05:30)
A Streetcar Named Marge - S4-E2
Continuity mistake: When Maggie fires the dart onto the locker, it's position in relation to the vent slits changes between the long and close up shots. (00:14:30)
Kamp Krusty - S4-E1
Continuity mistake: At the breakfast table, Homers plate of food changes entirely between shots. (00:02:50)
Brother Can You Spare Two Dimes? - S3-E24
Continuity mistake: When Marge says that the money was a blessing, and they can't waste it, the arm covers on the chair change size between shots. (00:10:40)
Brother Can You Spare Two Dimes? - S3-E24
Continuity mistake: At the start of the awards ceremony, Mr Burns and his podium emerge from nowhere on the stage. (00:07:20)
Continuity mistake: When the band is talking to the audience about being the 6th member of Spinal Tap, the water on the stage simply vanishes between shots. (00:06:55)
Continuity mistake: When we see Homer in the car for the 1st time since the band hit the stage, he has his hand up in the exterior shot but in his bag of crisps from the interior shot. (00:05:20)
Continuity mistake: When Marge tells Otto to get a job, the books on the bookcase by Otto change/move between shots. (00:16:50)
Continuity mistake: When Otto crashes the bus, there is no sticker on the bumper. When the bumper flies off, a sticker has appeared. (00:11:30)
Continuity mistake: When Bart realises Selma has 1 hour to live, the remote Patty is holding disappears as the camera zooms into Bart. (00:17:50)
Continuity mistake: When Bob is litter picking, the amount of litter by his feet changes drastically between shots. (00:03:20)
Continuity mistake: During the meal at the start, the food on Bart's plate changes between shots. (00:02:50)
Continuity mistake: At the dinner table, we see an overhead shot of the table and there is a glass of milk next to Homers hand. As the shot changes, this glass is now gone from that location and moved to nearer Bart. (00:02:50)
Continuity mistake: When Marge and Homer are arguing over his boyhood dream, the time on clock jumps forward between shots. (00:13:20)
Revealing mistake: When the bartender points to the Fudd neon sign behind him, his hand goes through the sign. (00:05:40)
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