Continuity mistake: As the power builds up in Bender, his left eye pops out, making him a cyclops, subsequently being eaten by the Cyclops eater. After the monster dies, Bender comes out, and has two eyes in the long shot, but puts his left eye back in the close up.
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Continuity mistake: In the first episode of season 6, "Rebirth", near the end after the real Fry comes out of the Rebirth chamber, the robot Leela says that she and the robot Fry are in love she now has the real Leela's mechanical arm device on. But she never had it before or after that shot.
Continuity mistake: Season 6, episode 19 "Yo Leela Leela": When Bender discovers Leela's secret writing place, throughout the entire scene the lipstick marks on his head keep changing places, sometimes disappearing and reappearing. Most noticeable is the one on the right side of his head: it disappears when he is shown from that side, then reappears as soon as the angle changes.