The location where Sterling Hayden proposes the deal to Kola Kwariani is a mock-up of the 42nd Street Chess and Checker Parlor in New York City. Director Stanley Kubrick was a regular chess player there as was Kola.
The narration was added at the studio's insistence. Stanley Kubrick hated the idea and thus makes much of the information that the narrator provides false or mistaken.
The total budget for the film was $320,000 - $200,000 was put up by United Artists, with the rest raised by producer James B. Harris. This was a paltry budget for a feature even by 1950s Hollywood standards.
This was the first film on which Stanley Kubrick worked with a cinematographer. Lucien Ballard was hired because Kubrick was officially working on a film union production for the first time which prevented him from using himself as the cinematographer, as he had done in the past. The two often did not agree on camera and lighting matters.
Stanley Kubrick:
[bathroom]
A gun is hidden in the locker room of the racetrack.
Stanley Kubrick:
[faces]
George Peatty, when he finds out about his wife's dalliance.
Stanley Kubrick:
[three-way]
Johnny Clay vs. George Peatty vs. Sherry Peatty.