Revealing mistake: At court, as Homer is walking towards Alec Baldwin, Kim Basinger and Ron Howard, Bart is in the background sitting with the rest of the Simpsons, but his head is missing from his body. His head then reappears back on his body after about 2 seconds.
Character mistake: Moe says that no women have been to his bar since 1979, yet in "Flaming Moe's" he hires a female waitress. Also, in the episodes "New Kid on the Block" and "Homer the Vigilante," Ruth Powers appears in the bar, and orders a beer in the former episode while Marge visited the bar in "Bart Gets Hit by a Car."
Plot hole: The director of Radioactive Man says to Bart "we found our new Fall Out Boy. That's what I would say if you weren't an inch too short. NEXT!" But Milhouse is the new Fall Out Boy, and he's blatantly smaller than Bart. Bart was standing right next to Milhouse, so the director could see the difference.
Continuity mistake: Ms. Krabapple takes the cellular devices from the children in her class and puts them in a Laramie Cigarette box. She dumps the box into a desk drawer filled with frogs. A few seconds later there is a shot of the class from her point of view with all of their cellular devices on their desks.
Factual error: In the scene where Lisa's great great grandmother, and the slave Virgil escape to Canada, they enter Canada across a suspension bridge, which has, on the Canadian side, the Canadian Maple Leaf flag. In 1860, Canada was not yet even a country, and the flag was the Union Jack and the Canadian Ensign. The Maple Leaf was not adopted as the Canadian flag until February 15, 1965.
Continuity mistake: Season 20, episode 16, "Eeny Teeny Maya Mo." In the scene where Moe is cleaning his window inside the bar, take notice that the size of the spot he cleans on the inside of the bar is small. But when the shot changes to the outside, with Moe and the others looking out from the inside, the clean spot is larger.