This episode seemingly contradicts the plot of "Lethal Inspection" where it is revealed that Bender has no backup and is in-fact mortal, suggesting it is possible for Bender to switch bodies with a robot that does have a backup unit.
The Professor's body is shown to be absurdly skinny. In previous episodes he appears to be pot-bellied, much like Fry, and - indeed - with his clothes on he continues to look somewhat pot-bellied.
In this episode, Fry seemed excited by the idea of having Leela's mind in Amy's body rather than reacting with disgust. This contradicts A Flight to Remember where at no point does Fry flirt with Amy, while he does so multiple times with Leela. Fry openly prefers a relationship with Leela to one with Amy- he even tells Leela that he has absolutely zero interest in Amy. This also contradicts Put Your Head on My Shoulders where Fry got sick of Amy and proceeded to panic after she said that she really enjoyed hanging out with him. Throughout the series, Fry is shown to have lower standards for looks of women for casual / no strings sex, than for relationships and pursues the beautiful Leela for a relationship but only saw Amy (who is clearly not attractive )as casual sex material.
Bender uses the professor's mind switching machine to occupy Amy’s body, and attempt to seduce the guards to a crown he is attempting to steal. This contradicts "A Flight To Remember" as well as other episodes throughout the series where it is implied that Amy is decidedly unattractive. At no point on-screen, does Fry flirt with Amy, while he does so multiple times with Leela.
When everyone switches back to their original bodies at the end of this episode, Hermes' body out of nowhere and with no explanation reverts back to its original weight, shape and size despite how Amy lost weight in Hermes' body.
