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The film's working title was I'll Take Manila. According to Hollywood Reporter news items, the title was changed "in view of the situation in the Pacific which deflates the value of this pun." The film started production before the United States' entry into World War II. By the time of the film's release, in May 1942, the Philippines had fallen to the Japanese and the destination of the ship in the film was changed from Manila to Puerto Rico. One of the film's songs, "I'll Take Tallulah," was also changed from its original title, "I'll Take Manila." According to various news items in Hollywood Reporter, director of photography Robert Planck shot the dance numbers that were added to the film in late December 1941. Retakes were shot by Clyde DeVinna, according to Hollywood Reporter, which also noted that because both Bert Lahr and Virginia O'Brien were ill, stand-ins had to be used for some insert shots.
According to various Hollywood Reporter news items, the film was originally to co-star Eleanor Powell and Robert Young. In mid-July 1941, it was announced that Desi Arnaz was being borrowed from RKO for a role in the film. In September 1941, Hollywood Reporter stated that Tony Martin was set for a "singing lead" with Powell and Red Skelton. It is possible that the role intended for either Arnaz or Martin was removed from the script, or changed for Frank Sinatra. Although Sinatra sings in the film, he has no dialogue. Another Hollywood Reporter news item included Donald McBride in the cast, but he was not in the released film. Ship Ahoy was Sinatra's first film at M-G-M, the studio at which he was under contract for much of the 1940s, following a brief period of being under contract to RKO. One number shot but not used for the film, "I Fell in Love (With the Leader of the Band)," by Jule Styne and Herb Magidson, was included in M-G-M's 1945 film The Great Morgan.