The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Audio problem: When Homer is putting Christmas lights around the outside of the house, he falls from the roof. You can then hear Lisa and Bart sarcastically clap. But you can see they both have their hands by their side, and no-one is clapping. (00:04:55)
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)
Other mistake: When Homer is giving people tartar sauce at the cafeteria, he says "plenty for everybody" with his mouth closed at the end of him saying it. However the photo in the newspaper is shown with his mouth open. Also, for the last part of "everybody" his mouth doesn't move.
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.
Deliberate mistake: When Homer is watching Weird Al's parody of his song, he never turns the t.v. on and it isn't already on, but somehow it turns on.
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.
Deliberate mistake: When Homer pushes the trampoline off the cliff, there is no rock below the falling trampoline. However, in the shot at the bottom a tall rock is visible which was drawn there on purpose for the trampoline to bounce off of, despite not being visible in the first shot.
Bart Gets Hit By a Car - S2-E10
Revealing mistake: After Marge has been in court, Mr Burns' lawyer says "Thank you very much Mrs Simpson", and when he does it, the top of his head above his glasses is less pale than the rest of his face.
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.
Scuse Me While I Miss the Sky - S14-E16
Audio problem: In Declan Desmond's film of Springfield Elementary shown at the end, Kearney and Dolph start beating Jimbo up. After Kearney says "Sellout," he says "Yuppie" in Dolph's voice. Then Dolph says "Soccer Mom" but in Kearney's voice.
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 VI - S7-E6
Factual error: In "Nightmare On Evergreen Terrace", Martin has a dream, in which he speaks Latin. At one point, he says a verb that doesn't exist: "morire". The words is "mori" (to die), "moritur" (noun dies) or "moreris" (you die). The "moirie" is also on the blackboard behind Martin. (00:08:20)
Diatribe of a Mad Housewife - S15-E10
Plot hole: Dr Marvin Monroe says to Marge he was gone for a long time because he was sick. That's impossible because he died in a previous episode and you can even see his tomb in the episode where Maud Flanders dies. [It could be argued that Monroe really was sick. It was never explained how he died and no one mentioned that he really was dead. The grave, the hospital named after him were in the simpsons universe with the belief he was dead. The clip show mentioned his death but alluded any specifics. As Marge mentions she thought he was dead and so could everyone else on the show.]
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