During the filming of scenes with the topless "slave" girls rowing the ship, the actors kept deliberately flubbing their lines just so they could watch the girls.
After watching rushes from the first day of filming, Peter Sellers leapt to his feet and said "Thank God we caught it in time!" He felt his performance was so bad that the movie should be cancelled. He was eventually persuaded to continue.
Two of the writers were John Cleese and Graham Chapman of Monty Python fame. The Python sketch "The Mouse Problem" was written for this movie, but was rejected by Peter Sellers.
According to biographer Roger Lewis, during filming Peter Sellers tried to have fellow comedian John Cleese fired from the production. This was due to the leading man's concerns that Cleese's performance would outshine his own. In the end, Sellers instructed that Cleese's screen time be reduced from the final version.