When the traffic cop brings Darkwing (in Gosalyn's body) home and is talking to Gosalyn (in Drake's body), you can see the outline of Darkwing's face mask on Drake's face.
In the first scene, Darkwing's mainframe computer changes size from smaller before Gosalyn appears to be huge after she shows up.
During the anti-gravity scene, Gosalyn and Darkwing mouth the same line in Gosalyn's voice.
Steelbeak: (On the phone) No, I won't accept a check! What am I, a drive-in deli? (Hangs up) Sheesh! What is it with these world leaders? Don't they keep an extra trillion around no more?
(Darkwing is in Gosalyn's body trying to reach a switch) Darkwing: Launchpad, I need your head. Launchpad: (In Honker's body) Now there's something I don't hear every day.
Darkwing Duck: I am the butter that burns in your pan!
Tupperware Quakerware is a parody of tupperware, a brand of storage container made of plastic.
James Bond The concept of Steelbeak could possibily be a reference to another James Bond character, Goldfinger, as that name combines a the name of a metal with a body part. Or it may be a reference to the James Bond character Jaws, a 7 feet 2 inch (2.18 m) tall villian with steel teeth. He appeared in the films The Spy Who Loved Me and Moonraker.
Trading Places The title 'Trading Faces' seems to be a reference to the 1983 John Landis film Trading Places. The film has two people, one rich the other poor, who switch lives.
Freaky Friday A movie (1976 and a remake in 2003) in which a mother and daughter switch bodies.
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