On an Island with You(1948)

There's music! There's dancing! There's romance! M-G-M's Big All Star Musical!

A young navy lieutenant is brought in as technical adviser on a song-dance-and-swim film being made by screen star Rosalind Reynolds. Having once done a number with her at a Forces show, the young lad somehow believes she should be his girl. Her boyfriend is just one of those disagreeing.