Continuity mistake: In the Wiggum's house the parent's bedroom changes style several times. When it is first seen the cupboard is opposite the door (When Chief Wiggum is looking into the room after climbing the stairs). Then it is on the wall running across from the doorway later when Chief Wiggum enters the room. When the Chief puts the Police Master key on his bed post the doorway is behind the bed and the bed is opposite the cupboard. Later when Bart steals the key the bed is seen parallel to the doorway.
Continuity mistake: After Bart and Ralph have just visited the cake shop they have chocolate and icing all around their mouths. Also they are carrying the 'Newly Weds'. In the next shot where they walk around the corner the chocolate, icing and model bride and groom have all disappeared.
Continuity mistake: When Homer is sitting watching cable, the rest of the family comes home and one of them is carrying a plant in a pot, which is put down next to the couch. While they watch and watch cable, it grows very tall and then withers down. When Homer goes behind the TV and starts kissing the wires, the plant has moved to next to the doorway and is suddenly fully grown again.
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)
Continuity mistake: When Bart is unpacking his things from the box, if you look at the mantelpiece, we can see that there is a candle on the right hand side of it. But later on, there is a candle on the left hand side which wasn't previously there. (00:02:30 - 00:03:15)
Character mistake: When Homer discovers that the Leftorium is going out of business, there is a sign that says 'Coming Soon: Gum for Less' beside the store. Later on, though, Ned says the new store is becoming 'Libertarian Party Headquarters.' (00:15:50 - 00:19:15)
Deliberate mistake: When Bart and Edna are watching "Holes" in the IMAX theater, Edna sighs and pulls out a locket which we can see the back of. After opening it up to reveal pictures of her and Seymour, we find out its actually a triptych when she opens up another image of Seymour's mother. From the way she unfolds this extra picture, Seymour's mother would have had to be facing outwards, but in the previous shot the back of the locket was blank.
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.