Homoerotic Subtext: At one point Jerry-as-Daphne seems to be developing genuine romantic feelings for Osgood, much to Joe's consternation (and we later find out that Osgood is completely unfazed by Jerry's real gender). On a side note, Joe and Jerry are Heterosexual Life-Partners, Joe is very insistent that they do everything together and that what's Jerry's is his and while Jerry vocally objects, he goes along with it anyway.
Though the last case may be more akin to them being like brothers, with Jerry being the little brother who gets bullied into doing things he doesn't want to.
Meganekko: Sugar believes that men who wear glasses are more gentle and vulnerable. Joe takes full advantage of this by dressing up as a bespectacled millionaire, though he behaves more like a Stoic Spectacles.
Recursive Crossdressing: Joe flip flops between being Joe, Josephine and Junior so many times, it's a wonder he doesn't have split personalities by the end of the movie.
Skewed Priorities: When the Mafia shows up at the hotel, he's more interested in saying goodbye to Sugar (and giving her their only source of money, a diamond bracelet, as a going-away present) than in getting the hell out of Dodge before they get murdered.
Unsympathetic Comedy Protagonist: He comes across as a total sleazebag who is not above lying, theft and even cruelty to children just to get into Sugar's pants.
Can't Get Away with Nuthin' : She claims that everyone in the band drinks, but she gets in trouble for it most often. When a flask falls out of her dress at the end of the "Runnin' Wild" number, it takes a fib from "Daphne" to keep her from getting kicked off the train.