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.
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)
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)
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)
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)
Answer: You are thinking about episode 20 of series 2 - "Anthology of Interest I". She technically never kills anyone, but in the episode she ask a "What if machine" (one of the Professor's inventions) what would happen if she was more impulsive. The machine then shows the more impulsive Leela killing off the Professor to get the money from his will and thereafter killing Hermes, Bender, Scruffy, Cubert, Nibler, Amy and Zoidberg to cover it up. Finally she does something really impulsive with Fry.
Andreas[DK]