Continuity mistake: At the very start the twins are stood facing each other. Camera cuts to behind and now they are side by side. (00:01:20)
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: When Lisa asks "What did you get?" when holding the tray, you can see next to her there is a cup, but in the next shot the cup has changed into a glass of milk.
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: When Lisa is speaking to Bart in the kitchen at the start of the episode, Lisa's hands are on the kitchen top. In the next shot, they aren't. (00:00:25)
Continuity mistake: When Skinner is showing Homer the "fake" sick note, the writing is clean and tidy. When we see Skinner comparing the note to the cheque the handwriting is suddenly different. (00:07:15)
Continuity mistake: The writing on the wall changes style and location from when Bart writes it to when Homer walks by. (00:03:00 - 00:06:30)
Continuity mistake: At the start Marge's tiles go from on the table to in her hands when Homer chases Bart. (00:02:55)
Continuity mistake: When Homer chases Bart at the start, the book that Lisa had has disappeared from her hands and she is now holding her tiles. (00:02:50)
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Mr Burns tells Homer to wreck something, Homer throws a plant pot onto the floor and it breaks into several pieces. When Mr Burns tells Smithers to take him home, the pieces of the broken plant pot are nowhere to be seen.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Marge carries the plate with a cover on to Mr Burns, you can see there is nothing by Bart on the corner of the table, but in the next shot a plate suddenly appears.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: During the dinner scene towards the end of the episode, Mr Burns puts his knife on top of the knife and spoon. Later on, the items of cutlery are now lying in a row.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When the family are having dinner with Mr Burns, you can see that Bart and Mr Burns have by their plates a fork, a knife and a spoon. In the next shot, the knife and spoon disappear.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When the cat comes out of the Simpsons' house, the doormat is blue. When Mr Burns goes into the house, the doormat is green.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Mr Burns knocks on the door of the Simpsons' house, there is nothing on the door, but in the next shot, a door knocker appears.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Homer knocks Marge off the bed, there is a small purple object by the lampshade. When she is back in bed, the object has gone.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Marge tells Homer that she's going to ringing doorbells for Mary Bailey, Homer says "Doh!" and there is nothing beside him on the table. In the next shot, a bowl and a cup have appeared.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: During the breakfast scene, the piece of toast that Homer is holding in his hand disappears.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Homer is eating his toast at the breakfast table, you can see there is nothing on the fridge behind him, but a quick cut to Marge, we return to Homer and a drawing has suddenly appeared.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: In the meeting with Mr Burns and his advisers, one of the advisers holds up a photo of a guy who dated Mary Bailey and the adviser's tie is green. When he is sitting down in the next shot, his tie is now yellow.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Mary Bailey has a group of interviewers around her her tie is blue, but in a close up of Mary in the next shot, her tie is purple.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Mr Burns is doing his TV commercial, the grass in the bowl of the three-eyed fish is light green in some shots, but in close-ups it is dark green.
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