The first draft of the screenplay was written by Bryan Forbes in 1960, when the story was designed as a vehicle for Cary Grant. He eventually dropped out of the project, which subsequently underwent many changes. It was eventually decided to make the girl the central character, and Shirley MacLaine was signed for the lead. After seeing The Ipcress File (1965), she suggested Michael Caine as her leading man, which led to still more re-writing to accommodate his working-class cockney persona.
Shirley MacLaine does not speak until twenty-nine minutes into this movie. In fact, she doesn't even appear to sing along with the other women during the opening song and dance number.
A "gambit" is a chess tactic where a player sacrifices a piece to get a more advantageous position in the game.
(At around one hour and fifteen minutes) Listen closely to the restaurant scene and you'll hear "Strangers in the Night", which was released that year, in a different movie.
Behind Shahbandar's desk you can see a painting by Picasso, the study of a young man's head in black and white, and on the right the portrait of a woman, probably a Renoir.