When the ship is crashing, Fry screams "We've lost power in the forward Game Boy! Mario not responding!", but it is seen he is holding an NES controller. There are SUPER GAMEBOY systems for SNES and N64, but not the NES, making that option irrelevant.
The size of the Nimbus varies - in other episodes, the ship is seen as city-sized, yet it crashes in a very small area in front of the laboratory, barely the width of the street.
When Bender is crawling out of the Cyclops-eater's mouth, he's briefly shown with his two eyes, while he's supposed to have only one. In the next scene, he only has one eye again, putting his second eye back in.
During the final scenes where the Leela-Bot says "Let's ditch these meat jackets!" and sheds her skin, the Wrist LoJack-a-mater (which the real Leela wears, but the Leela-bot does not) appears and disappears on her right wrist in the same shot.
In the last scene, the Professor and Fry effortlessly lift Bender up in celebration, which is an amazing feat considering he weighs 525 pounds.
How could the Professor use the Sphere-O-Boom to save Bender when it was already destroyed in "Bender's Big Score"? The answer could be that the professor had a spare one locked away which the nudist alien scammers could not get to (or given the professor's forgetful nature, he simply mislaid it).
The Leela-bot and Fry-bot shed their 'skin' at the episode's end, but their robot appearance is not the same as when they were created at the Build-A-Bot Workshop. (Perhaps, as in the Clockwork Origin episode, they have evolved.)
How did Zap survive the crash with his head intact when he did not have the professor's safety shield.