The D'oh-cial Network - S23-E11
Continuity mistake: At one point in court while everyone is laughing, Patty's hair is colored wrong. Her hair is a similar shade of color as Rod and Todd (who are sitting next to her) rather than her own bluish grey hair.
Revealing mistake: When Homer pushes the soda vending machine next to the candy vending machine, a large scratch appears near the upper right corner of the screen.
Suggested correction: This is in the questions as well. With the long amount of time the artists have to make an episode it's very hard that something like this would get by them. It's probably the device you watched it on.
Brother Can You Spare Two Dimes? - S3-E24
Other mistake: On the DVD, when Homer is sitting on the Spinemelter, he says at one point "I've tried to fill it with family, religion, community service, but those were dead ends. This card is the answer." However the subtitles say "I've tried to fill it with family, religion, but those things were dead ends. This card is the answer", leaving "community service" out.
Suggested correction: It is very common to shorten the subtitles so viewers don't have to read much.
Lisa's Pony - S3-E8
Corrected entry: When Homer falls asleep in the car, he hits the dashboard with his fist, and the airbag pops out. If you watch in slow motion though, he doesn't hit anything at all. (00:19:30)
Audio problem: When Patty says "Marry me Patty?" while reading Skinner's message, her mouth doesn't move.
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: Before Horst wants to talk with Homer, Lenny is standing beside the donut box, who wasn't seen in the shots before and after. (00:12:15)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: When Carl complains that he can't be fired, everybody behind him, Homer and Lenny has disappeared. (00:09:00)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: At the Tavern, when Homer slaps the money on the table, the white cloth that Moe was holding has vanished. (00:04:55)
Continuity mistake: When Moe tries the Flaming Homer, there are bottles that keep appearing, and the knife disappears suddenly. (00:06:55)
Like Father, Like Klown - S3-E6
Continuity mistake: At the end of Krusty's story, Homer changes from being in his tuxedo to being in his normal clothing. (00:10:10)
Suggested correction: It should be noted that a considerable amount of time has passed while Krusty is telling his story. Note the candles in the screenshot for example, they have burnt out during the story. Its reasonable to assume that there would have been a chance for them to change during this time.
Continuity mistake: While Homer is sleeping, his head is facing the 'Core temperature' indicater. When he wakes up, he is in a different position. (00:04:25)
Continuity mistake: At the beginning, when the bus is driving to the school, the streetlights outside disappear/reappear between shots. (00:01:30 - 00:02:20)
Continuity mistake: Bart puts his lucky red hat on the hat holder. It disappears in the next shot. (00:07:10)
Continuity mistake: When Bart crashes at the door of the Legitimate Businessman's Social Club, his head is facing the door. You can only see this for several frames. In the next shot, his head is facing the sky. (00:05:25)
Other mistake: When Bart sees that Santa's Little Helper ate his homework, and the camera moves really fast, you can see that the Krusty Doll and picture frame have vanished from the desk beside his bed. (00:00:55 - 00:01:50)
