At one point, a man is seen fixing a new sign on the door of the deceased's office, reading "Powell, Crane and Ross". This is an in-joke -Norman S. Powell was the show's production supervisor, Barry Crane the production manager and Bill Ross the supervising art director.
When he first meets Captain Burke, Danny Swift sings "Dum de dum dum", the beginning of the opening theme music of the TV series "Dragnet."
In the dialog between Captain Burke and Charlie Who, there are numerous references to the famous "Who's on First" comedy routine, but never mentioning Abbott & Costello, who performed it. They were "some other guys" to Charle Who.
Les refers to the vaudeville "Two a day", which was a term describing acts that played two performances a day. This was actually the highest level of vaudeville for top performers. Lesser acts would have to perform three, four, or even five times a day.
Burke refers to Miss Bumpsy Cathcart as an "ecdysiast", which is a fancy name for a stripper. Gypsy Rose Lee, who plays Cathcart, was probably the most famous stripper in the history of burlesque. She was the subject of the musical "Gypsy".