Continuity mistake: When Homer is preparing the barbecue, he is wearing an apron that says "Mafia staff apron". After he goes to pick up the lighter fluid, it reads "Maffia staff apron", and after he has lit the barbecue, it is back to saying "Mafia".
Continuity mistake: After the aliens have dropped off the Simpsons in their back yard, Marge is seen wearing her usual red pearls. Except in the final shot of the family. Then her pearls are white. This is not due to the alien light source altering the colors in the segment, because Marge's pearls have been a dark color through the whole episode, even inside the alien spaceship.
Continuity mistake: In "Hungry Are The Damned", when the family are looking up at the UFO and Homer says that the burgers are getting cold, the burger he is eating has a bite out of it. In his close-up it is a whole burger.
Continuity mistake: When Bart is unpacking his things from the box, if you look at the mantelpiece, we can see that there is a candle on the right hand side of it. But later on, there is a candle on the left hand side which wasn't previously there.