While riding in the Rolls Royce, West asks Burke what noise she hears and is told it is the electric clock. This is a reference to a Rolls Royce advertising campaign that said a Rolls was so quiet that when you drive it all you can hear is the clock ticking.
Vera refers to her showgirl number and Burke says it was "on a velvet swing". This is a reference to Evelyn Nesbitt, a Ziegfeld Follies showgirl known as "the girl in the red velvet swing", who was in the middle of a love triangle that ended in a murder.
John Ericson, Steve Forrest, Nancy Gates, Louis Hayward, George Nader, Jan Sterling and Anne Francis all receive 'Special Guest Stars In Alphabetical Order' credits. (Francis, of course, is not in alphabetical order; she receives the coveted "And" billing after the others.)