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.
As stated in the mistake, It happens when ANY magnet is attached to him.