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: Bender couldn't have flushed his chest down the toilet, it wouldn't have fitted. (00:11:50)
Correction: We never see Bender flush his chest. His chest could have been broken down into component parts that would fit and then reassembled. It might be unlikely that he put himself back together correctly (since he said he threw away his instruction manual), but flushing his chest down the toilet is not out of theoretical possibility.
Corrected entry: Bender didn't get affected by the magnet on the can opener. Normally he gets crazy and sings show tunes. (00:01:10)
Correction: Magnets on his head only affect his inhibition, thus allowing him to sing showtunes; they don't automatically make him sing. The can opener opening his head was probably significant shock to distract him from singing.
Corrected entry: When Leela and Fry find Bender in the sewer, he doesn't have his head on right and one of his legs and an arm is attached in the wrong place. He says that he can't put himself together properly because he threw away his instruction manual. In every other episode he can reattach his head, legs or arms with no problem.
Correction: However in every other episode Bender is only reattaching one specific limb or his head - in the sewer he had to reattach all four limbs plus his head, a much harder proposition.
Correction: This is not a mistake. At this point in the series, Leela's parents are still trying to keep their distance, and not let anyone know that Leela is a mutant.