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: There are three mistakes when court is dismissed: 1) the people standing around disappear, 2) the two men with Fat Tony disappear for one shot, and 3) when Bart says that crime doesn't pay, Marge is suddenly standing beside Bart. (00:20:35)
Continuity mistake: When the Simpsons are eating for the second time the alien on the very left, which previously had spots on his cheek, now has no spots.
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)