The title (and synopsis found online at various websites) of this episode does not fit what actually happens. When Archie wakes up to find himself in bed with the girl, the joke on him (played on him by a buddy) is not that he believes they got married while he was drunk, but rather that he had sex with her. There's no mention of marriage at all, so there's never another "wife." In fact, Archie explains to the girl that he's happily married and what they supposedly did was wrong.
Danielle Brisebois doesn't appear on this episode.
This episode reunited Harvey Lembeck (Wally) and Allan Melvin (Barney Hefner). Both were regulars on The Phil Silvers Show (Sgt. Bilko) from 1955 to 1959. Lembeck played Cpl. Barbella, and Melvin played Cpl. Henshaw on Bilko. Lembeck had played one of Edith's class mates on "Edith's Class Reunion" (1972).