Continuity mistake: At the very end of the episode, when Homer is being carried off by the crowd, you can see that the crowd carrying Homer, the people are small, so you'll have to look closely, but right before the credits, Marge's necklace changes from red to white, back to red and then finishes with white all in one shot.
Continuity mistake: When Bart is standing on the bench, Jimbo and Milhouse are standing in the front row, on the right side of the screen. But when there's the closeup (a second later), there are children shown in front of Jimbo and Milhouse and the girl with the purple hair is gone.
Continuity mistake: When the Stonecutters are singing "We do", the position of several characters, particularly the Martian and Chief Wiggum, change randomly as the camera angles change. The Martian starts at the end of the table on the right side, with Chief Wiggum two seats to the left of him. In later shots, the Martian, then Wiggum are both switched to the same position, midway up the left side. Then, when the song ends, Wiggum has disappeared, and the Martian remains in this new position.
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.