Lisa's Pony - S3-E8
Continuity mistake: When Lisa calls Homer at work, Homer picks up the phone on his left side. Instantly after, we see him hang the phone up on his right side. (00:19:00)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: After Lisa declares world peace, when the two UN guys hug each other, the United Nations symbol on the wall has changed from purple to blue. (00:05:25)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: When Homer picks up the monkey's paw for the first time, a person walks behind him. He has disappeared in the next shot. (00:02:35)
Continuity mistake: When Bart is trying to get the toilet water to flow the other way, the toilet can't refill that quickly with that number of flushes.
Secrets of a Successful Marriage - S5-E22
Continuity mistake: When Marge is shopping at the Kwik-E-Mart she puts a red can and a blue can on the counter.When Apu tells her about the offer on hair dye he puts two blue cans into the paper bag.
Kamp Krusty - S4-E1
Continuity mistake: In the shot where Kearney is reading the letter sent by Marge whilst he is eating the jellybean cookies, there is a quick shot of Kearney's hand going to his mouth with the cookie to eat it. Note that there is nothing on his wrist. In the next shot where it is revealed that Kearney is reading the letter rather than Bart or Lisa, he has spiky, black collars on his wrist. (00:14:25)
All's Fair in Oven War - S16-E2
Continuity mistake: Right at the end when James is at the toll booth, we see him wearing a watch on his left hand, then when he's handing the money to the toll booth man, he is not wearing it, then when the shot changes he's wearing it again. (00:20:35)
Fat Man and Little Boy - S16-E5
Continuity mistake: In "Fat Man and Little Boy," Homer, while playing with Malibu Stacy, picks up Lisa and runs away from The Front door, which is behind him. In the next shot, however, Homer runs out of The Front door and into the street.
Tree House of Horror IX - S10-E4
Continuity mistake: In "Starship Poopers," Kang always wears a glass thing on his head, but whenever Homer beats him up, it's gone.
All Singing, All Dancing - S9-E11
Continuity mistake: In the scene where Snake first comes in to shoot the Simpsons, after they sing, he starts singing. When turns his head then turns it back, he blinks and his eyes disappear.
Treehouse of Horror XIII - S14-E1
Continuity mistake: When everyone has been turned into animals, Police Cheif Wiggum, as a pig, takes off his tattered shorts and throws them into the fire. Later in the scene he's magically wearing them again. (00:19:40)
Continuity mistake: When Marge is throwing all the Krusty merchandise into a bag, the bag changes from grey to brown between shots.
Continuity mistake: When Cletus takes a picture of one of the robots at the parade, the old lady next to him changes from black to white between shots.
Tree House of Horror V - S6-E6
Continuity mistake: In 'Time and Punishment,' in the basement, as soon as Homer puts the back of the toaster back on, two pink wires taped to the side of the toaster suddenly appear. (00:09:30)
Continuity mistake: The extension cord Jimbo is using for a belt disappears after they run around the corner of the corridor whilst chasing Bart.
Continuity mistake: When Krusty is telling his daughter that he lost her violin, keep an eye on the door of the appartment. A grey bar appears and disappears on the door underneath the "eyeglass" between shots.
Continuity mistake: When Homer is walking and talking with Hank Scorpio when he first arrives at work there is reversed "J" on Homer's tie that comes and goes between shots.
Tree House of Horror V - S6-E6
Continuity mistake: When Skinner is cooking the kids, he and the cook are chasing Bart, Lisa, and Milhouse. From the back, he has an apron tied around his neck. In the next shot, he puts on an apron.
Tree House of Horror X - S11-E4
Continuity mistake: In the flashback, the car moves a lot further than it did originally after hitting Ned.
Continuity mistake: When Lisa is helpfully explaining what a Bar Mitzvah is, Krusty's new puppy loses its red lead. (00:07:30)
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