Continuity mistake: At the beginning of the show, the hospital Mr. Burns is at has a sign in front of it that reads, "Got Tumor?", but when we see the hospital again it isn't there. Additionally, the "Mayo Clinic" sign atop the building gets noticeably smaller in the second shot.
Continuity mistake: When one of the pockets of Marge's coat explodes (when Homer is stealing the rare Gummi), a huge pile of candy comes pouring out. When she bends down to pick some up, there isn't nearly as much candy there as before. There are people picking up the candy with her, but they would have to pick it up extremely fast, and they aren't.
Continuity mistake: When Homer has been informed about the Christmas money being spent on Bart getting his tattoo surgically removed, he leaves the house. When he opens and closes the door to leave, the wreath on the door is white with a red bow. When Homer then turns to look his Christmas decorations, the wreath is now green. (00:08:50)Hamster
Continuity mistake: As Homer is giving his speech to the dressed up monkeys, all of the monkeys are dressed in blue suits and you can also see there is one monkey next to the stairs on the stage. In the next shot of Homer leaving the stage there is now six monkeys, with only one wearing a suit and it is grey. (00:19:45)Lummie
Continuity mistake: In 'The Thing and I' when Homer and Marge return from driving around in the rain, there is no doorknocker on the door. Then in the shot where Hugo escapes, we see the door open with red scratches on it, and there is a doorknocker. Then later when everyone leaves to find Hugo, it's gone again. (00:02:40 - 00:04:55)Hamster
Continuity mistake: Homer points out to Marge that now that the kids are away, he has grown two more hairs, making it four on the top of his head. Later when they are reading Lisa's letter, he has two hairs again. But later still when they are watching TV, he has four again. Two of them fall out when he see that Bart is the ringleader, leaving him with his original two.
Continuity mistake: As Marge arrives home and sees the bullet holes in the door, the shot changes to a POV shot from behind the door and you can see there are some changes in the holes. The first change is there are three bullet holes on the right hand side which are all the same distance from each other, when she enters the middle hole has moved closer to the bottom one. The other change is the large hole in the middle of the door. On the bottom right hand side its shape goes from being a little irregular to a more round shape. (00:16:20)Lummie