Corrected entry: In the sewer, the guy with the big forehead starts singing with his guitar and a crowd gathers around. But you can see Leela's parents standing in the crowd and having no reaction to their daughter whatsoever, despite them knowing what she looks like. Considering later episodes, this is a bit confusing.
Corrected entry: The sergeant refers to Fry's grandfather Enos by his first name, something that would never happen. A superior officer - especially a non-com - would refer to him as "Fry", "Private" or "Private Fry". No army sergeant ever referred to an enlisted man by his first name.
Corrected entry: This has to be done in slow-motion to actually notice. When Morgan and Hermes first meet they give each other a paper to stamp. It's already been established that a bureaucrat stamps forms five times, but, if you watch the scene in slow-motion, when Hermes gives Morgan a form to stamp and Morgan gives Hermes a form to stamp, Hermes stamps the form he was given 3 times and Morgan stamps the form she was given 2 times. Then when Hermes gives Morgan back her own form and Morgan gives Hermes his own form, Hermes stamps his own form twice and Morgan stamps her own form once. They both should have stamped both forms five times.
Corrected entry: The part of the Lunar Module that Fry and Leela go inside shouldn't be there, the astronauts would of used it to get back to the CSM orbiting the moon. The whole thing lands on the moon but the cabin, the bit where they go in, should actually be floating in space somewhere after they had jettisoned it.
Corrected entry: In the final part of the "tear-jerker" sequence at the end, the pizza shop owner is seen to be elderly and walking with a stick. The sequence starts the day after Fry was frozen (when the pizza shop owner appeared to be middle aged) and is only supposed to last 12 years - the pizza shop owner ages too fast.
Corrected entry: Often while traveling through space, we can see the stars in the background moving (as if the Futurama cast were in a car and the stars were street signs). This would not happen in reality, unless one was traveling relativistic speeds (even then, the motion of the stars would look very different). Instead, the stars should be still (the sun doesn't appear to move when you're out walking).
Corrected entry: The other poker players confront Bender about his cheating using X-ray glasses, and he grabs the poker chips off the table and runs. What's the point of that? The other players know he's been cheating and they won't cash the chips - they are worthless plastic.