Continuity mistake: When Homer and Sideshow Bob are chasing the mechanic on stilts, the mechanic tries to get away, and his cape falls off while he is being chased. In the next shot, we see a close-up of the mechanic, and you can see his red cape is back on again. Then in the next shot, we see Homer and Bob chasing him, and his cape is off.
Continuity mistake: When Burns first shows the team the nerve tonic, the "&" on the 'Brain & Nerve Tonic' label is facing backward, but as Burns pulls it away it faces forward. Then as he moves it around as he's talking, the "&" switches between facing forward and facing backward again. This happens all in the one shot.
Continuity mistake: In Hungry are the Damned, when The Simpsons are on the spaceship and the aliens show them the food, there are 3 pots and two plates. Yet when the shot changes there are 4 pots and no plates.
Continuity mistake: When the Simpsons are eating and the family are praising Marge, Homer's plate is first seen to have a small amount of yellow food and a bit of pink food (meat?).In a later shot when Homer steals and uses Marge's pepper spray he has a large pile of yellow food.
Continuity mistake: In "The Thing and I": After the kids have found Hugo in the attic, when Marge and Homer return home, both front door knobs (inside and outside) do not have backplates, but once Hugo escapes both door knobs have backplates. The two backplates vanish and reappear repeatedly in following shots. It's funny because when they leave to search for Hugo, Homer shuts the door with no backplates, but then Bart uses a key in the backplate to lock the front door.
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.