Other mistake: In the scene set in the future after Lisa, as the US President, held a conference with some journalists, just before the scene changes they show a black journalist with eyes not drawn among the crowd.
Other mistake: When Homer pretends to read the newspaper, the back page is very noticeably blank and missing any print. (00:08:00)
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)
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?
Other mistake: When somebody throws a cola can at Homer, the can never hits the ground.
Other mistake: When Bart is looking at Doctor Hibbert on the rowing machine, all the pictures on the walls behind him don't have faces on them.
The Dad Who Knew Too Little - S14-E8
Other mistake: When Bart flashes Lisa's laser at Principle Skinner's bottom, Chief Wiggum can still see it even when his car is in the way.
Guess Who's Coming to Criticize Dinner - S11-E3
Other mistake: In the German version, the Italian cook peeved by Homer's comment on lasagna swings the cleaver at him using an Italian word ("Porcodio") which is a rather strong blasphemy, way stronger than any other expression used in original or in other localizations worldwide.
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