Continuity mistake: When Apu awakes, he has a closed note pad, and the table looks small. In the next high-angle shot, Apu's book is open and face down, with paper on top of it and a pen beside it. The table is also bigger, with Bart sitting there with his breakfast things too.
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.