Continuity mistake: When Homer gets mad when Carl calls him "Chrome Dome", there is a fish stick on his plate, but in the next shot, the fish stick has disappeared.
Continuity mistake: When Homer is speaking to Carl and Lenny at the coffee stand, there is initially nothing in Lenny's cup, but a few shots later his cup is now full without him filling it.
Continuity mistake: Flanders is seen signing the agreement with his right hand. In later episodes, he is known for being left-handed.
Continuity mistake: The colour of the school changes from yellow when Martin and Bart are talking before the test to grey when Bart has spoken to Otto about being held back. (00:07:00 - 00:11:00)
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.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When the man turns over the picture of Mary Bailey on the flip chart, the words "Artists Conception" are missing.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: During the meeting, Mr Smithers is sitting by Mr Burns and you can see there is nothing in front of him, but when the camera angle changes to behind Mr Burns in the next shot, a glass has suddenly appeared.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When we see the picture of Mary Bailey on the flip chart, the wording "Actual Photo" underneath the picture changes position between shots.
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