Continuity mistake: In front of Krusty Burger, when Lou carries a naked Bart to the sign post, the post is embedded directly in the concrete walkway slab, just beside the left corner of the patch of grass. Once Bart is cuffed, the sign post has actually moved down about 4 feet, and is also now embedded directly in the grass at the right corner. In following shots, it's at the left corner of the grass and then right again.
Continuity mistake: When President Schwarzenegger tells Russ Cargill he will have to go back to making family movies, there is a "Diaper Genie" promo poster on the Oval Office wall and on the immediate left of President Schwarzenegger's desk. But the promo poster disappears and the walls of the Oval Office become further from the desk in the next long shots.
Continuity mistake: When Maggie does her disappearing act through the sinkhole, and Marge rushes to get Homer, the wooden porch swing is directly in front of the window, with its top beam as high as the top of the window. When Homer says, "This dome can play tricks on you," note the door and window behind Marge, because the swing is now gone.