Home Away From Homer - S16-E20
Continuity mistake: Ned's front door before he and his family leaves opens on the left side (when looking at it from outside), but after the "Coach" has moved in, it opens on the opposite side.
Home Away From Homer - S16-E20
Continuity mistake: When Homer tries to leave his seat in the cinema and complains about eating the apple, the shot shows his body fat has wedged him in the seat. However we can see from all the shots before this that the fat was never wedged in like it was when he was trying to leave.
Home Away From Homer - S16-E20
Continuity mistake: When Homer hits Coach with a chair, the white stripe that was on Coach's tracksuits has gone.
Home Away From Homer - S16-E20
Continuity mistake: When Homer meets Coach for the first time (and maybe another point in the episode), the position of Ned's house's window frames to the side of the door change between shots.
Home Away From Homer - S16-E20
Continuity mistake: We see Coach cutting down trees in Flanders' former driveway. However there had never been any trees in Flanders' driveway.
The Bonfire Of The Manatees - S17-E1
Continuity mistake: When Marge is in the car upset at Homer, the door to their house changes from open to closed then open again between shots.
The Girl Who Slept Too Little - S17-E2
Continuity mistake: At the end of the episode where Homer is on the field talking to Buck the baseball player, the stadium is crowded. When Homer and Marge are leaving in their baseball golf car one second later, the stadium is empty. (00:20:40)
Milhouse Of Sand And Fog - S17-E3
Continuity mistake: Homer's chicken pox disappear when he puts the food into the suitcase.
Treehouse Of Horror XVI - S17-E4
Continuity mistake: At the end of "B.I.: Bartificial Intelligence," Homer climbs onto the ceiling and turns his head in a parody of "The Exorcist." He then lets go and lands on the bed. The only problem is that his body landing doesn't match the position it would from what we see on the ceiling. If he dropped down his face should be face down, body facing up and his head would be closer to the end of the bed. When he lands, his head is near the pillows, his body facing down and his head facing up.
Continuity mistake: When Homer says to Bob that he tells Marge everything, his hand is by his mouth, the shot cuts and it is at his side.
Homer's Paternity Coot - S17-E10
Continuity mistake: When Dr. Hibbert is about to reveal the results of the paternity test, Mason Fairbanks is wearing a blue blazer and black pants. But, when Dr. Hibbert points at him and says "This guy", he has a light blue sweater and blue pants.
The Seemingly Never-Ending Story - S17-E13
Continuity mistake: When Lisa pets the goat after it returns her necklace, her pink jacket is missing, in the next shot, she has the pink jacket on.
Continuity mistake: When the jury is "oohing" Wallace Brady, Lenny's five o'clock shadow is missing. It reappears in the next shot.
The Mook, the Chef, the Wife, and Her Homer - S18-E1
Continuity mistake: Just as Otto is about to put in the grand funk tape you can briefly see an different tape in the recorder. Slow motion is not needed but a sharp eye is.
The Mook, the Chef, the Wife, and Her Homer - S18-E1
Continuity mistake: When Bart and Fat Tony's accomplices are going to meet Krusty, Krusty's nose can briefly be seen as white when it should be red.
The Mook, the Chef, the Wife, and Her Homer - S18-E1
Continuity mistake: When Lisa grabs Ottos tape recorder her necklace is orange but when she gets off the bus it is white.
Please Homer, Don't Hammer 'Em - S18-E3
Continuity mistake: It is revealed that Bart is very allergic to shrimp. However, in "The Frying Game" (where Marge and Homer get "framed" for a murder and end up on "Frame Up"), Bart says he was in the green room and that he "ate so much shrimp."
Please Homer, Don't Hammer 'Em - S18-E3
Continuity mistake: As the workmen begin to leave site after hearing that Homer is unable to pay them, a couple of tools are dropped on the ground; however, in the following shot, facing back towards the cabinet where Homer is hiding, the tools have disappeared.
Please Homer, Don't Hammer 'Em - S18-E3
Continuity mistake: In this episode Principal Skinner breaks into Bart's doctors office to find out if Bart has a 'kryptonite'. Bart discovered Skinner was allergic to peanuts. On Bart's medical history form under 'known allergies' it has shrimp ticked (they later battle with shrimp and peanut on a stick). However in a previous episode (The Heartbroke Kid, season 16 episode 17) it was discovered that he was allergic to cauliflower, so that should have been on the list as well.
Continuity mistake: When Homer is eating donuts while everyone is doing push-ups, his donut stays the same size every time he bites it.
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