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?
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.
Character mistake: When Chief Wiggum shows up to arrest Nelson during the game at the end of the episode, Bart goes with Wiggum instead while pretending to be Nelson. Even a cop as incompetent as Chief Wiggum would not have mistaken Bart for Nelson since he'd had numerous dealings with both before this episode; Wiggum may not be particularly bright, but he knows who's who in Springfield.
Factual error: When Bart is at Nelson's house and Nelson is firing the BB gun, bullets should come out of his gun when he pumps it. None ever come out, and several times he is shown firing without pumping.
