Continuity mistake: The old men beside Grandpa when Homer plows the retirement home switch places, depending on whether it's a long or a close shot. (00:10:00)
Continuity mistake: As Homer is giving his speech to the dressed up monkeys, all of the monkeys are dressed in blue suits and you can also see there is one monkey next to the stairs on the stage. In the next shot of Homer leaving the stage there is now six monkeys, with only one wearing a suit and it is grey. (00:19:45)
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)
Tree House of Horror VII - S8-E1
Continuity mistake: In 'The Thing and I' when Homer and Marge return from driving around in the rain, there is no doorknocker on the door. Then in the shot where Hugo escapes, we see the door open with red scratches on it, and there is a doorknocker. Then later when everyone leaves to find Hugo, it's gone again. (00:02:40 - 00:04:55)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When Maggie is driving Homer's car, a man is behind him. He is seen waving his left arm but when the shot changes to Maggie he is waving his right arm. (00:14:50)
Continuity mistake: When Homer is having the thanksgiving dinner at Moe's, he isn't wearing a tie, but between shots he suddenly gains a tie. (00:20:35)
Kamp Krusty - S4-E1
Continuity mistake: Homer points out to Marge that now that the kids are away, he has grown two more hairs, making it four on the top of his head. Later when they are reading Lisa's letter, he has two hairs again. But later still when they are watching TV, he has four again. Two of them fall out when he see that Bart is the ringleader, leaving him with his original two. (00:15:35)
Tree House of Horror VII - S8-E1
Continuity mistake: In 'The Thing and I' when Lisa and Bart are questioning Homer about the 'thing' up in the attic at breakfast, Homer is the only one eating. But in the next shot you can see Lisa and Bart with breakfast too. (00:01:30)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: When Mr Burns is bowling outside with other old people confronting him, he drops the ball in front of him. In the next shot the ball is further away from him. (00:15:00)
Continuity mistake: When Homer enters Moe's tavern, Moe is playing solitaire. The cards on the table are face down/face up between shots. (00:04:45)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: When Bart and Lisa argue over which wish to make, the hand on the table changes position, and the thumb switches sides. (00:03:30)
Homer's Triple Bypass - S4-E11
Continuity mistake: When, Lisa bangs on the window of the operating theatre, there is a person sitting behind her who is asleep. However, when she shouts to Dr Nick, the people behind her are completely different. Then she sits down again, and the sleeping person is behind her. (00:20:00)
$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Continuity mistake: As Marge arrives home and sees the bullet holes in the door, the shot changes to a POV shot from behind the door and you can see there are some changes in the holes. The first change is there are three bullet holes on the right hand side which are all the same distance from each other, when she enters the middle hole has moved closer to the bottom one. The other change is the large hole in the middle of the door. On the bottom right hand side its shape goes from being a little irregular to a more round shape. (00:16:20)
Lisa's Pony - S3-E8
Continuity mistake: When Homer is phoned by Lisa, the color of the phone is blue. Immediately after, it turns to green. (00:19:00)
Like Father, Like Klown - S3-E6
Continuity mistake: When Krusty has a cigarette during the cartoon just before he is reunited with his father, he keeps his cigarette pack in his shirt pocket, 'close to his heart'. When Krusty and his father hug, the cigarette and the packet are gone.
Continuity mistake: When the family is having dinner, the glasses on the table keep disappearing/reappearing between shots. (00:09:30 - 00:10:30)
Continuity mistake: When Lisa shows her exam to her family, the "a" note keeps changing from being circled in red and in a red round. (00:04:30)
Continuity mistake: When the family is at dinner, there is a top down view which zooms in on them from above. In this shot there is no newspaper on the chest (to Homer's left). In the next shot of Homer a newspaper has appeared. (00:07:50)
Continuity mistake: At the end of the episode, when we see a wide shot of everyone going to join Ned on the hill (and singing the song) look to the far left. You will see Apu - and his skin is yellow.
Springfield Connection - S6-E23
Continuity mistake: When Marge sees Homer's car parked illegally over 3 handicapped spots you can see a car parked near Homer's that is orange. Later in the scene when Marge starts writing a ticket up for Homer the car next to Homer's is now a dark brown. (00:14:35 - 00:15:05)
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