Continuity mistake: The guardrail at the Springfield Gorge keeps changing between shots when Bart is about to make his big jump; in the first wide shot there is a short rail opposite the "stone ramp." Then in the Bart-POV shot from atop the ramp, the rail is much longer, and the parking lot and picnic area behind it have disappeared. And when Homer is actually jumping the gorge, the rail disappears altogether.
Continuity mistake: In the beginning after Maggie hit Homer on the head, it shows him laying on the couch with Bart & Lisa on the left. The next shot it shows the TV, in the next shot it shows Homer on the left sitting and Bart & Lisa on the right. It's impossible for Homer to get up and switch sides with Bart And Lisa in less than 5 seconds.
Other mistake: When Marge is being questioned, before she says 'If you don't have anything nice to say, then don't say anything at all', there is a shot over her shoulder looking at the blue haired lawyer. Not only is he (the lawyer) there directly in front of her, but he is also sitting on the bench with Burns. In all other shots his chair is empty as it should be.
Continuity mistake: During Marge's testimony, Lionel Hutz has a neat stack of papers in front of him the whole time. But in the close-up when Homer and Hutz both cover their eyes in sorrow, Hutz has several pieces of crumbled paper and a broken pencil in front of him. The was not nearly enough time for him to make such a mess since the last shot of him.
Continuity mistake: While Homer and Barney are smoking in the boys bathroom, when Principal Dondelinger walks in on them the "boys" sign on the exterior side of the door disappears in the closeup, but the sign reappears as Dondelinger exits. The door push plates on both sides of the swing door also vanish/reappear during the scene. (00:04:35)