Character mistake: Before their first performance, the director of "La Boheme" wishes Homer good luck. To anyone in professional theatre, doing so is the cardinal sin of theatrical superstition and is never done; the appropriate phrase is "break a leg."
Brother From Another Series - S8-E16
Continuity mistake: In the shot where Homer yells, "Marge, I'm going to look for the kids," their door is shut. After Homer sees the wave and runs back inside, their door is open all of a sudden.
22 Short Films About Springfield - S7-E21
Other mistake: When Chalmers and Skinner are having lunch with hamburgers, Chalmers bites it. When he opens it, the bread's slice is bitten but the meat is not.
Other mistake: When Moe is calling for a 'Hugh Jazz' there is a shot of the bar and Otto can be seen in the upper right corner. However his face is all distorted and out of proportion. (00:14:30)
Continuity mistake: When the robbery happens, Homer steps on the robber's feet, and we can tell he has large shoes. When they show video of the robbery on the news, the robber has regular shoes. During the hearing, they watch the video again. His shoes are back to long again.
Revealing mistake: When Nelson is offering Lisa the fraction quiz answers, right before Lisa says she's never cheated before and won't again, her right hand disappears for a single frame.
Other mistake: After Bart complains that Jonathan Harris isn't Dr. Smith, Harris says for Bart to meet him in the food court. Then the Robot says "Danger Bart Simpson, danger." How did he know Bart's name?
Marge vs. the Monorail - S4-E12
Revealing mistake: When Homer is driving along and singing, he passes three houses in the background. Those exact same houses reappear three times in the same shot even though he never turned around. (00:01:15)
Homer's Triple Bypass - S4-E11
Continuity mistake: When Krusty bursts into the room, the shot ends with him having his arms and legs bent. In the next shot, he's straight as a ruler. (00:15:10)
Simpsons Bible Stories - S10-E18
Plot hole: Somehow, despite being enslaved and being nowhere near anything that could help them, the Jews have a camel, which we did not see coming across the channel.
Continuity mistake: When Homer says he's going to the cinema, we see his drinking bird working in front of the computer. It makes a key press on the lower right of the keyboard, however on the following close up shot of the bird pressing the Y key it is a standard qwerty keyboard layout.
Continuity mistake: When Sherri and Terri raise their hands and say "like us Mrs. Krabbapple" they raise their hands over their heads. Camera cuts and their hands are a lot lower. (00:04:20)
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: In Homer's flashback, when the pimp chases Homer, who is covered in garbage, Homer runs away from him on one side of the street. When Homer runs on the other side of the street, he is not covered with garbage. When he climbs a ladder and falls into a manhole, he is covered with garbage again.
Continuity mistake: When the teacher is looking out of the window, Bart has his paper in front of him on the desk. The paper disappears in the next shot, but reappears when Bart takes Martin's paper off the table and puts it on his desk. (00:06:10)
Who Shot Mr. Burns? (1) - S6-E25
Revealing mistake: Right at the beginning, watch as Principle Skinner enters the classroom, there's a clock on the top left hand of the screen. The majority of the left side of the clock is not drawn in.
Tree House of Horror V - S6-E6
Continuity mistake: In "Nightmare Cafeteria", a teacher walks into the classroom and sees Bart sitting at his desk facing backwards. At this point, you can see the lockers behind the teacher are white, but in the next shot they are blue.
Tree House of Horror V - S6-E6
Continuity mistake: In "Nightmare Cafeteria", when Bart is being served his lunch at the lunchroom, his tray is initially plain but in the next shot it is now divided into six squared segments.
Tree House of Horror V - S6-E6
Continuity mistake: In "The Shinning", Homer is eating a bag of crisps while sitting on the sofa and you can see "Potato Crisps" logo on the bag is coloured red, but in the next shot it is now blue.
Continuity mistake: The comic book guy should be seen on the ground when Bart comes to the music store, but he has disappeared.
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