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.
The New York invasion sequence was filmed in Manhattan on a Sunday morning, accounting for the city's empty streets.