From All Movie Guide  
This lesser Astaire/Rogers vehicle is one of several screen versions of the venerable Hubert Osborne stage play Shore Leave. For reasons unknown, Fred and Ginger are virtually supporting players here, spending most of their time trying to patch up the romance between Fred's fellow sailor Randolph Scott and Ginger's sister Harriet Hilliard (better known as Harriet Nelson, of Ozzie and Harriet fame). One of the sillier aspects of the plot hinges on raising enough money to renovate a broken-down old ship; to do this, Fred and Ginger stage a lengthy musical number that must have cost five times as much money as they raised! But that number, a languorous dance rendition of Irving Berlin's "Let's Face the Music and Dance", compensates for all the nonsense that has gone before. One fringe benefit of Follow the Fleet is spotting two fresh-faced starlets named Betty Grable and Lucille Ball. Hal Erickson