Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: When we see Homer eating at Marge's birthday dinner at Singing Sirloin, there is a cake on a dish and a wine glass by his plate. When we see Homer a little later on, the cake and wine have disappeared and there is now an ordinary drinking glass by his plate.
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: When Homer opens the door with his present, look at the door knocker and you can see that is a completely different one to the one seen at the start of this episode.
There's No Disgrace Like Home - S1-E4
Continuity mistake: When undergoing shock therapy, the doc raises his hands to his head. They are not present in the next shot. (00:19:00)
There's No Disgrace Like Home - S1-E4
Continuity mistake: When Homer walks in on the family eating dinner, Marge has her feet on the second cushion of the sofa. Camera changes and now they are on the third cushion. (00:08:50)
There's No Disgrace Like Home - S1-E4
Continuity mistake: When they put Maggie down in the Creche she is in the middle of a carpet. Camera cuts and now she's at the edge. (00:04:25)
There's No Disgrace Like Home - S1-E4
Continuity mistake: The amount of marshmallows in the jelly at the start changes between shots. (00:02:00)
Continuity mistake: On the bus at the start there are some lines on Mrs. Krabbapple's microphone. They disappear when she tells Bart to sit down. (00:03:00)
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.
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