Continuity mistake: As people throw stuff at the redneck bar, the guy who introduces Lurleen is leaning to his left then instantly to his right between instant cuts. (00:06:10)
Continuity mistake: After Lurleen sings 'No-One Understands You', she puts on her apron and picks up a tray. On the tray, there are three bottles of beer. But in the next shot, Homer goes over to Lurleen, and there is only a cup. (00:07:15)
Continuity mistake: When Marge and Homer are arguing over his boyhood dream, the time on clock jumps forward between shots. (00:13:20)
Continuity mistake: When Lurleen is in the studio with the Simpson family, Homer has his arms crossed. When Bart asks to do a solo his hands are now in his pockets. (00:14:50)
Continuity mistake: In the scene where Homer decides he wants to stay with Lurlene, she locks the door about 3 times before going to kiss Homer, but when Homer leaves, he just opens the door, he doesn't unlock anything.
Continuity mistake: When Homer and Marge are entering the cinema, Marge is taking Maggie with her. But when watching the film, Maggie is nowhere to be seen.
Continuity mistake: When the family are driving home from the cinema, Bart draws an angry face on the back of Homer's head. It is never there at any other point in that night.
Continuity mistake: After the dinner with Sideshow Bob, Patty, Selma and the Simpsons, the food on Bart's plate changes between shots. We first see a piece of meat with some peas, then we see two pieces of meat and some mashed potato. It changes randomly throughout the scene. (00:02:40 - 00:07:05)
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 Bob is telling his story about picking up rubbish on the side of the road, we see Bob in The Front of a line of people. When we see the convicts in the reflection of the trooper's sunglasses there is someone in front of him. (00:03:20)
Continuity mistake: When Bob is litter picking, the amount of litter by his feet changes drastically between shots. (00:03:20)
Continuity mistake: The way the chapstick is held out for Bob in prison changes from one shot to the next. (00:04:40)
Continuity mistake: When Selma tells Bob not to worry about the cost of the wedding she has a cigarette in her hand which disappears almost instantly when she grabs Bob's hand. (00:10:40)
Continuity mistake: When Marge spots Krusty, from the regular view, Krusty's hand is down on the table. But from the view from the camcorder, his hand is on top of the cake. (00:14:00)
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: Selma says she wants a separation while leaning forward with her arms behind her. Camera changes and she is stood with her arms closed. (00:18:40)
Continuity mistake: During the wedding, look at the man with the blue hair carrying the tray with hors d' oeuvres that Homer is eating. When Homer says "Hey wiener boy. Where do you think you're going?" the man's collar changes from white to black instantly.
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 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)
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