Revealing mistake: When Marge is speaking on the phone to her sisters, her sisters say something that sounds like they said that Homer is ugly. Marge then puts down the phone wire that she was curling round her finger. You can temporarily see that the phone wire disappears when Marge puts it down. It is at the very end of an early scene, because as soon as this happens it changes to another scene. (00:04:40)
Revealing mistake: After Homer brings Santa's Little Helper home, Homer and Marge hug, and if you look behind them, the background is upside down. There is a picture hanging upside down, and there is a lamp which seems to be hanging from the ceiling. Then in the next shot, the background is normal. (00:21:40)
Revealing mistake: When Bart makes a copy of his photo for Lewis, footage of Milhouse inserting a coin into the copy machine is used. You can see Milhouse's pink shirt sleeve instead of Bart's orange shirt sleeve. This same shot is again reused a third time seconds later. (00:09:55)
Revealing mistake: While Homer is waiting for Marge to come downstairs, both Patty and Selma are wearing turtlenecks. When Homer thanks Mr. Bouvier, in the next wide shot as the twins nod their heads, both of their turtlenecks are not colored in properly at their torsos, so the background is visible through their bodies. (00:16:30)
Revealing mistake: When Homer is imagining being locked in the jail cell and he turns around to find he is in his own home, he turns to look at his family. There is a close up shot of his terrified face, and the people in the background watching the game (I think it might be Lenny and Carl) have no eyes. The rest of their face is fine, but their eyes are missing.