Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: At work, the salad in Homer's sandwich disappears when he mentions that 'she' made it.
Continuity mistake: When Bart says "Everybody, come quick!", the fridge door goes from open to closed.
The Last Temptation of Homer - S5-E9
Continuity mistake: When Bart has had his throat sprayed, we see him standing up just before the shot changes to the power plant. The shine on his shoes instantly disappears and reappears several times.
Continuity mistake: After Homer dodges the cannonball near the end of the episode, the blue platform that he stood on goes further away from the edge of the stage between shots, and when Homer hugs Marge the platform has disappeared and Peter Frampton's cooler has become closer to Homer.
Continuity mistake: The offensive baseball cap that is in the Kwik-E-Mart changes from green to blue during the episode.
Treehouse of Horror XV - S16-E1
Continuity mistake: At the beginning when Kang and Kodos's boss comes to have dinner, his stomach explodes leaving a hole, yet in the next shot the hole has vanished. (00:00:40)
The War of the Simpsons - S2-E20
Continuity mistake: When Homer has caught General Sherman he beats it with an oar so that the oar snaps in two. Then suddenly Homer rows with both oars intact.
The Great Louse Detective - S14-E6
Continuity mistake: When we see the picture collage of Moe with the pickle jar the bottom picture is of them in front of the pyramids. When it pans around the pictures though, it turns into a picture of them on the beach.
Treehouse of Horror XIV - S15-E1
Continuity mistake: The piles of sweets and candy that Bart and Lisa have at the start vanish in the wide shots when Homer arrives.
Continuity mistake: When Krusty enters the Jewish Walk of Fame building, there are no stars on the pavement outside it. When he leaves there are. (00:06:15)
Continuity mistake: When Homer writes an autograph for Ralph at the restaurant, Lisa is sitting opposite Marge, has yellow liquid in her glass and has red and brown food on her plate. In the next shot, Lisa is opposite Homer, has a blue drink and has white and green food. (00:14:25)
Continuity mistake: When Homer leaves the studio after being cancelled there is no sign next to the door. When Marge walks up to comfort him there is now a 'stage door' sign there. (00:18:35)
Continuity mistake: When the pile of newspapers fall on principal Skinner, two garbage cans appear out of nowhere beside the door. (00:19:10)
Continuity mistake: In the episode "New Kid on the Block," Bart says his home address is 1094 Evergreen Terrace. In "Homer the Vigilante," his home address is 723 Evergreen Terrace; and for the rest of the series, it has been 742 Evergreen Terrace. (00:18:30)
Thirty Minutes Over Tokyo - S10-E23
Continuity mistake: When Homer breaks into Flanders's house there's a shot of the refrigerator and nothing is on it. In a closer shot, there are tickets being held up by a magnet.
Tree House of Horror XII - S13-E1
Continuity mistake: In 'Hex and the City', Marge and Homer swap places at the wedding.
Tree House of Horror V - S6-E6
Continuity mistake: In 'Time and Punishment,' when Homer exits the basement, he discovers Bart and Lisa are giants, and he then screams and runs back to the "basement" - however the same door that leads to the basement seconds ago, now leads to a green -carpeted room, and the basement seems to have vanished. The door is also hinged on the wrong side. (00:12:50)
Continuity mistake: When Homer is talking to Ned about having his own BBQ Ned is facing the fence but in the next shot he is facing alongside it with his head turned to Homer.
Continuity mistake: When Homer and Bart are at the cabaret show, Mr. Burns and Smithers are there with two women. In almost all of the shots there is a woman sitting between Burns and Smithers, except in the close-up of them when Burns asks "How does he DO it?". Then Smithers is shown as sitting right next to Mr. Burns. (00:21:00)
Homer vs. Lisa and the 8th Commandment - S2-E13
Continuity mistake: At Sunday school, Milhouse's jumper changes from black to red 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