Episode Two: The Series Has Landed - S1-E2
Other mistake: When the Moon Patrol officers throw Bender out of the airlock onto the moon's surface, they are exposed to hard vacuum, but they aren't wearing space suits. Throughout the episode it is established that the moon's "atmosphere" is a vacuum and protective suits are necessary - when the farmer removes his helmet he begins to asphyxiate instantly.
Other mistake: A few of the liquid people are shown wearing clothes; while you can usually see through the people to the walls, etc, behind them, you can't see the clothing through them. (00:11:10)
I, Roommate - S1-E3
Other mistake: When the crew are leaving Fry's new apartment, Amy slips on the banana skin again and falls over, and for some reason Fry tries to shut the door without her leaving. Maybe it was easier than drawing her getting up, but still worth a look. (00:15:30)
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.
Other mistake: When the robots are building a Tetris wall, there is a section on the left made up of two red 'L' bricks. However, the upright L block is not the same as the other red blocks, because it is flipped laterally. (00:09:05)
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.
A Big Piece of Garbage - S1-E8
Other mistake: When Professor Farnsworth was presenting the crude drawing of the Smelloscope to his scientific peers, he wiped the napkin which it was drawn on on his forehead, causing all the ink to smudge. But why isn't there any ink on Professor Farnsworth's head? (00:05:30)
Bender Should Not Be Allowed on TV - S5-E15
Other mistake: When Fry says "Hey Bender" 3 times he then picks up the phone and says "Hey Bender" but watch carefully and you'll see he doesn't pick up the phone he just reaches out and suddenly has it.
Lrrreconcilable Ndndifferences - S6-E11
Other mistake: When Lrrr is looking at his reflection in the clothing store, the necklace he's wearing is seen as it appears normally, not reversed as a mirror image should be.
Attack of the Killer App - S6-E3
Other mistake: As the Antarians are stripping Bender, the hinges for his door are shown on the left. However, the hinges should be on the right.
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.