Bender Gets Made (a.k.a. Bendfellas) - S2-E17
Other mistake: The strap for Leela's eye-patch on the right side of Leela's head (from her perspective) goes just over her ear. The left side goes above her ponytail. This would prevent the two ends of the strap from meeting.
Bender Gets Made (a.k.a. Bendfellas) - S2-E17
Other mistake: At the end, when Fry, Leela and Bender are sitting at the table, Fry's legs disappear (and the gray blotch beneath him isn't them - it's the table leg; and it's not hiding them either - his knees should be visible behind it). (00:21:35)
Other mistake: After Hermes has limboed under the door he is being told off by LaBarbara. Amy is standing next to her but her nose is missing. From front on her nose is usually a half circle.
Put Your Head on My Shoulder - S2-E10
Other mistake: When Fry is talking to Leela (After being stitched onto Amy's body), he asks for some privacy from Amy, who puts her fingers in her ears and begins singing a song in Chinese. At one point, when it shows a close-up of Fry's head, you can barely see Amy's head, and the finger disappears and reappears near her nose, then suddenly reappears back in her ear.
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.