Continuity mistake: Bart is thrown onto his front yard from Sideshow Bob's limo. The campaign buttons pinned to Bart's shirt by Bob's goons in the previous shot have disappeared.
Continuity mistake: Homer draws a face on a punching bag. He starts to show Bart how its done. The punching bag has its eyes filled in now.
22 Short Films About Springfield - S7-E21
Continuity mistake: Lisa comes out of the hairdresser's with a new hairstyle which Nelson laughs at. She is walking away to Nelson's right yet when Nelson's being chased by a tall man later and flees around a corner to his left she's suddenly standing there.
Continuity mistake: Apu grabs the ham and crosses out of the expiration date with a thick black marker. When he places the ham on the shelf the black marker cross out is gone and the writing on the pack looks perfectly printed as before.
Character mistake: Burkina Faso is listed as being among the Southern Hemisphere locations Bart called when Homer is looking over the phone bill; since Burkina Faso is completely within the Northern Hemisphere, it would have made no sense for Bart to call there.
Suggested correction: It may not make sense, but Bart isn't exactly the sharpest tool in the shed. In this same episode, he looked at his globe and thought Rand McNally was a country and was convinced by Lisa that the citizens there wear hats on their feet and that hamburgers eat people. Additionally, he could have just decided to prank call someone there if for no other reason than he thought the name of the country was funny.
Entirely possible, but since Bart had a globe right there to refer to, even someone with his limited geographical knowledge would have been able to tell that Burkina Faso is in the Northern hemisphere, unlike the other locations he did call as depicted in the montage (Antarctica, Argentina, unspecified South American nation, etc).
Continuity mistake: The name card display stand on Homer's desk disappears after Mr. Burns interrupts him.
Continuity mistake: The bikes disappear after Bart and Milhouse arrive at the cave.
Continuity mistake: When Mr Burns and Smithers are standing outside Springfield Stadium, Mr Burns says to Smithers, "Put a little smile on his card" and Smithers is writing it down with a pencil in his left hand. When the Simpsons arrive in the next shot, the pencil has changed into another piece of paper.
Continuity mistake: When Bart says to Homer that he's on "Jumbo-Vision", the man behind Homer is drinking from a paper cup with a straw, but when we see Homer on the screen, the paper cup has disappeared.
Continuity mistake: After Lisa unlocks the bathroom door with the coat hanger, the puddle of "baby blood" (Pepto-Bismol) at her feet disappears in the next shot.
The Trouble With Trillions - S9-E20
Continuity mistake: In the post office when Chief Wiggum is using the megaphone, Otto is seen in the right line as seen from the door but when Kent Brockman attempts to interview him he is magically in the other line, in front of Krusty.
Kamp Krusty - S4-E1
Continuity mistake: Bart holds up his maths book but in the next shot the book is on the desk. (00:05:00)
Continuity mistake: When Moe is wiping the beer glass at the beginning of the episode, the glass is initially smooth but changes to dimpled in the very next shot.
Tree House of Horror III: The Simpson's Halloween Special III - S4-E5
Audio problem: In King Homer, after Burns and the guards on the island rush through the doors, you hear Burns say "Shoot him in the groin and belly!" But his mouth doesn't move. (00:10:30)
Elementary School Musical - S22-E1
Other mistake: As Stephen Hawking rotates in circles, his front wheels stay locked in a straight position, rather than turning into the turn.
Elementary School Musical - S22-E1
Other mistake: As Lisa and Marge drive out of Brooklyn, they see a mural painted by the two artists. As the camera looks at Lisa, the mural reflection should be reversed, but isn't.
Continuity mistake: When the students have to practice square dancing in the gym, Lisa spots a male student and there is a red circle next to her on the floor where she is standing. When the teacher tells Lisa she has to dance with groundskeeper Willie, the circle has disappeared.
Continuity mistake: When Lisa arrives home after her parents gave the boy a party, she parks her bicycle near the path. When Lisa sees the boy with make-up on his face in the next shot, the bicycle is on the grass.
