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: When Otto is playing the guitar with bart in the middle of the night, there are close-ups of Otto whenever he is singing. You can see that the wall behind him is plain. However, when there is a wide shot of otto and bart, the wall behind otto has two tables leaned against them. (00:15:50)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: When Homer purchases the monkey's paw, you can see open desert to the right of Homer. There was a building in its place a few shots earlier. (00:02:30 - 00:03:15)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: When Homer is at the vending machine, in certain shots he is wearing a tie and in others he isn't. (00:02:20)
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.