At no point is the navy that Charles Laughton, Cary Grant and Gary Cooper belong to named. That the officers are English and others American would not make sense in the British or U.S. navy, but no flags or emblems are seen, and their uniforms belong to no known country on earth.
This is the only film featuring both Gary Cooper and Cary Grant as the movie's leading men but they don't appear together onscreen. However, in Alice in Wonderland (1933), Grant played the Mock Turtle and Cooper played the White Knight, having their only movie scene together (of sorts) as the entire cast appears in the tea party scene.
In 1932, Tallulah Bankhead told an interviewer that she only accepted this role so that she could "f*ck Gary Cooper."
Charles Laughton has an "and introducing" credit for what was his seventh film.