Treehouse of Horror XVIII - S19-E5
Continuity mistake: When Marge puts the logo Hugh Laurie in the microwave, he splatters in the corner. Next shot the splatter is in the middle of the microwave. (00:01:00)
Continuity mistake: When Homer has his car towed from the bank, it is hooked up at the rear. When they arrive at the impound lot, it is hooked up at The Front.
Continuity mistake: When Marge is watching Homer's "Margarine" music video, the coffee in her cup keeps changing.
Continuity mistake: When Homer is in his mansion watching Weird Al's parody of his song, the trash on his floor (frappuccino cups, pizza boxes, etc.) keeps switching places.
Continuity mistake: During Sadgasm's first appearance, a girl with a green skirt, a red sleeveless shirt and grey hair moves from place to place during the "concert."
Continuity mistake: When Homer lights his albums on fire, he watches Weird Al doing a parody of his song. When it's over, the fire is gone and there are no ashes where it would be.
Continuity mistake: When Sadgasm is making their first appearance, Homer says, "We are Sadgasm," and there are a few students walking around, but when he says, "And this song is called 'Politically INcorrect'," there is a big crowd in front of them with no time to form one.
Continuity mistake: As Bart is about to enter his house after trying to impress his friends by krumping, you can see he is entering The Front door. However, in the next shot when he gets inside and Marge is waiting you can see that he has entered the family room, which is only accessible through the back door. Entering by The Front door would place him by the stairs, at The Front of the house.
Continuity mistake: This episode rewrites the entire backstory of Marge and Homer. For starters, Lisa and Bart were both not born yet, despite the fact that in the episode "Lisa's First Word," the '84 Summer Olympic games were being broadcast, and Bart and Lisa were both there. In this episode, Homer and Marge were just dating, but again in "Lisa's First Word," they were married and living in their Evergreen Terrace house. Additionally, Maggie was born in the episode "And Maggie Makes Three." Homer also lost all his hair in that episode, yet in this episode in the early 90's he still has a full head of hair.
Continuity mistake: When Stefan starts crying at the football, Marge puts some music on and Homer's Sadgasm band appears on the radio. At this point, Stefan's wine glass is in front of the couch on the floor. Stefan then says he needs whale songs - Marge puts an "Oceans of the Sea" CD in the CD player and the wine glass in front of the couch suddenly vanishes.
Eternal Moonshine of the Simpson Mind - S19-E9
Continuity mistake: Near the end, when Homer says "I'm a genius", Krusty is seen with yellow skin, but is later seen with his usual white skin.
Continuity mistake: When Bart says "Stop feeling sorry for him", Dr. Robert Terwilliger Sr. is seen sitting in the audience, even though he is supposed to be sitting in the witness stand.
Continuity mistake: When the school bus drops off Bart and Milhouse at the Simpson house, Bart puts his backpack on frontwards and starts krumping. When he walks through The Front door, he is still wearing his backpack on his front. It then cuts to inside the house, and we still see him coming through the door, but the backpack is gone.
Continuity mistake: When the men from Festival Cruise Lines arrive at the Simpson house, they park in the left-hand lane (closest to the house) with the car facing oncoming traffic, seen both when they first pull up and, more, in the background while informing Milhouse about his parents. But in the overhead shot of the house, the car is parked the other way around, following the direction of traffic.
Treehouse of Horror XVIII - S19-E5
Continuity mistake: When Marge shoots Chief Wiggum, the arrow goes through his tie. When they roll on top of him, the arrow isn't through the tie anymore.
Continuity mistake: In the surgeon's office there are three certificates on the wall with ribbons on them. In the first shot there are two red ribbons and a blue one but in the shot where Homer stands up to read the bill all the ribbons are red.
Love, Springfieldian Style - S19-E12
Continuity mistake: In the third story of the episode, Bart and Nelson throw Martin into the Jukebox despite it never being opened. When he is trapped inside the box the glass is firmly in place as well.
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