Continuity mistake: At the garbage man debate, when Homer says 'Then you should have been early.', we see a shot of Lenny laughing. To the right of him, there is an old woman. In the next shot of Chief Wiggum, the same old woman is sitting to the right of him. In the later shot of Wiggum, Miss Hoover is sitting to the right of him and the old woman has disappeared.
Continuity mistake: When Ray Patterson's / Homer's office is shown, the text on the door is different according to the different shots. When the shot is on the door, the writing on the window (Name and Sanitation Commissioner) is close together, but when the shot is from inside the office with the door open, the writing is apart.