Jack Arnold soon learned that Peter Sellers did his best work on the first take and was usually useless by take three. The actor, schooled in improvisation, couldn't keep the lines fresh if he had to say them over and over.
Peter Sellers made this film in part as a means of emulating his hero, Alec Guinness, by playing multiple roles in one movie.
The Marseilles and New York harbor sequences were filmed in Southampton, UK. The presence of the Queen Elizabeth ocean liner there was a lucky coincidence.
Jack Arnold did not ask the studio's permission for the Columbia Pictures logo joke (the Torch Lady runs after seeing a mouse), convinced they would say no. Studio executives only heard of the joke when they attended the New York previews, where it got a huge laugh. Thanks to that that, there was no thought of cutting it, though it is absent from some television prints.
While filming, Peter Sellers was acting on stage in the comedy Brouhaha, which also dealt with a mythical kingdom whose ruler develops an outlandish plot to secure U.S. aid. Five days a week, he had to be at the studio at 6:30 a.m. for makeup and wardrobe, then get himself to the theatre by 7 p.m. During location shooting, a driver picked him up at the theatre after the performance and he slept in the car on the way to the film shoot.