Continuity mistake: Abe's girlfriend dies in the middle of this episode, but at the end, seconds before the end credits, you can see her walk behind some other old people.
Continuity mistake: In the scene where Lionel Hutz hands over the $106 check, Abe Simpson's room number is 18. After Abe called Homer, the manager of the Retirement Castle comes in. The number 18 has now disappeared.
Revealing mistake: When Bart and Lisa enter the H2WHOA! ride, Lisa's eyes disappear for a few seconds. (00:03:30)
Audio problem: After the donut delivery guy asks Carl why all the donuts are piling up, Carl responds with Lenny's voice.
Continuity mistake: When Mr. Burns and Smithers go to leave, the beak-like knocker has disappeared from the Simpsons' front door.
Continuity mistake: When Marge goes in front of her painting after it is uncovered she stops with her head in front of Mr. Burns' genital area. In the next shot, her head is shown in front of Mr. Burns' hand.
Continuity mistake: In the scene where Bart and Homer find Marge's paintings in the attic, there is a shot of the paintings all stacked up and you can see that the edges of all of them are the same shade of pink as The Front painting. However, when the boys flick through the paintings, the backgrounds and edges are a variety of colours, including pale blue.
Continuity mistake: After Lisa paces around the school hallway practising how to ask Mr. Bergstrom over for dinner, when she opens the classroom door there's a backplate behind the doorknob and a lower panel under the window, but when she sees Miss Hoover and gasps, the backplate and lower panel have both disappeared. (00:13:35)
Continuity mistake: When Lisa opens the classroom door (opposite the teacher's desk) and is shocked to see Miss Hoover has returned, note the door opens outward (into the hallway) and the doorknob is on the right side of the door. When Lisa runs out of the classroom, that door now opens inward and the doorknob is on the left side of the door. (00:13:40)
Continuity mistake: When Miss Hoover returns to class she writes "psychosomatic" on the blackboard, but when Lisa runs out of class the word has vanished from the board. (00:13:55)
Revealing mistake: When Marge is yelling at Homer at the dinner table after Lisa goes to her room, the outline of Marge's mouth over her neck when her lips are moving shows the neck line in her lips. (00:18:50)
Other mistake: While Homer is in Lisa's bedroom trying to make things right with her, there are three pictures taped to Lisa's mirror. After Homer tells her the music may help, in the next shot Homer walks over to stand behind Lisa. Those pictures taped to Lisa's mirror are weirdly behind Homer's reflection, as if the pictures are taped to the wall behind Homer. Three shots later, when Homer tells Lisa he can fix the dollhouse, his reflection is accurate in relation to those three pictures taped to the mirror. (00:19:20)
Continuity mistake: When Mr. Bergstrom and Homer are eating together, Mr. Bergstrom's left hand is up and holding a fork, but the next shot shows his left hand resting on the table.
Continuity mistake: The long shot of Homer and Mr. Bergstrom eating lunch together at the childrarium shows Mr. Bergstrom's left hand resting on the table, but the next close-up shot of the duo shows Mr. Bergstrom's left hand up, holding a fork.
The War of the Simpsons - S2-E20
Revealing mistake: When Maude Flanders says 'Oh, okay' to Homer after he asks for peanuts, the lipstick on her lips briefly flickers and disappears for a few frames. (00:04:56)
The War of the Simpsons - S2-E20
Other mistake: When Ned says "crème de cassis" while describing what was in the drink he made, there are several animation errors in this shot. His head is disconnected from his body, and his nose disappears. Also, a part of his face is missing between his fingers while he does the 'OK' hand gesture.
The War of the Simpsons - S2-E20
Continuity mistake: When Homer has caught General Sherman he beats it with an oar so that the oar snaps in two. Then suddenly Homer rows with both oars intact.
Three Men and a Comic Book - S2-E21
Continuity mistake: When Martin is tied to the chair near the end of the episode, the number of ropes tied to him change from four, then to three, and then back to four.
Three Men and a Comic Book - S2-E21
Continuity mistake: When Martin is tied up in the treehouse, at one point Bart takes the brick off the comic book and sets it down near Martin. When Bart and Millhouse fight, the brick disappears.
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