Trivia: If you watch closely, after Fry is leaning on the chair just after the countdown to ten reaches zero and he loses his balance, they cut to a close-up of the chair's legs falling over. You can see Nibbler's shadow cast on the wall in front of him. This was however retroactively added to the first season DVD. In the original airing of the pilot on TV Nibbler's shadow was not present.
Suggested correction: This has proven to be in the original airing.
Kif Gets Knocked Up a Notch - S5-E5
Continuity mistake: Zoidberg wasn't in the machine to begin with, yet he appeared later. When it spins you see the whole inside of the machine - he's definitely not there.
Suggested correction: They even make a comment about this, he lives there. So he was probably sleeping under the grate but still got ejected. There's parts of the floor we don't see.
Saturday Morning Fun Pit - S7-E19
Revealing mistake: Near the end of the "Bendee-Boo" segment, while everyone is laughing, one of the Harlem Globetrotters' (between Amy and Leela) right arm keeps disappearing and reappearing several times in one shot.
Suggested correction: It's on purpose like the rest of the fourth wall Scooby Doo animation references.
Other mistake: Bender wears a magnetic bow tie. However in series 1 episode 2 it's shown magnets screw up his circuits and make him sing songs. It's mentioned in a previous entries correction that it's only when the magnet is near his head. This isn't true as it's shown in others episodes that it happens when a magnet is attached anywhere on him.
Suggested correction: It's strong magnets near his head that mess up his inhibition unit. The bow tie is a very weak magnet.