The jukebox that S.Z. Sakall operates is a Jennings Telephone Music System jukebox. These now-rare machines provided songs by request over a telephone line hosted by a live operator. The transmission of music over a telephone line allowed for quicker turnover of songs and no physical (vinyl) media at the customer's location.
John Ridgely, who plays Mike Collins in this film, also played Eddie Mars in The Big Sleep (1946), released the same year and is playing in the movie theater within this film. Both are Warner Bros. pictures.
When Count Oswald is in Polly's apartment the interior lighting goes dim a couple times, which Polly says is a recurring problem. Oswald mentions his familiarity with such a scenario in a story whereby a husband was trying to make his wife think she's crazy by continually dimming the lights. This is a reference to the 1938 thriller play 'Gas Light,' written by Patrick Hamilton (British novelist and playwright), and adapted into the noteworthy successful 'Gaslight (1944)' movies in the 1940's.