Continuity mistake: During the conference, when the Professor is talking to Leela, Hermes's shirt buttons are not visible but in the next shot, his buttons are visible. (00:11:55)
Continuity mistake: After winning the demolition derby, one of the doors of the ship falls off, but when they get back to earth it's back on the ship. (00:09:15)
Continuity mistake: In the scary door, the hay stack on the barn it diagonal, but when the aliens are attacking, the hay stack is vertical. (00:13:30)
Continuity mistake: When Bender takes Nibbler's matter, the matter is not that big and it's the only matter he has in his compartment. Later when Doctor Perceptron goes to remove Bender's imagination, the matter can be seen through his compartment only now it is a lot bigger. (00:18:40 - 00:50:10)
Audio problem: When Mom goes to slap her kids after they fail to find Farnsworth, Fry and Leela, she slaps Walt but you don't hear it until she's halfway through slapping him. (00:47:30)
Revealing mistake: Throughout the Demolition Derby, most of the people in the audience are drawn without faces.
Other mistake: As Rich Little's head is doing the intro, the blond spectator to his right has messed up eyes, one normal, the other totally black.
Other mistake: When Leela is pumping dark matter, you see the lumps in the hose that's supposed to be the matter. But the nozzle is a regular nozzle, and the balls squeeze through easily, even though they're super-dense, and therefore solid.