During the "I'll Take the Water" routine, in which the sailors fill their mouths with water in order to spray Lou Costello, Costello actually cracked up and spit his mouthful of water onto the floor, but the take was so funny it was kept in the film.
About ten minutes into the movie, Pomeroy Watson (Lou Costello) gets a ticket for jaywalking. After the cop gives him the ticket, he and Smokey (Bud Abbott) turn around to go back to the base. They pass a baby carriage in front of a store window with a very young girl in it. Pomeroy stops and says, "Hey, Smokey, look at the cute kid". That "cute kid" is Costello's daughter,Carole Costello.
The group gets assigned to the USS Alabama and sets sail for Pearl Harbor, HI from San Diego, CA. With the movie being released on 30 May 1941, the real USS Alabama (BB-60) was commissioned on 16 Aug 1942 and earned nine battle stars during her service in World War II.
This movie was actually filmed after Hold That Ghost (1941), but they released it first because the public wanted to see some "service pictures." After this film was released, Universal revamped "Hold That Ghost" to add a romantic subplot and some musical numbers for The Andrews Sisters and Ted Lewis' band, which hadn't been in the original cut.
The trivia item below may give away important plot points.
When the picture was sent to the U.S. Navy for approval, they refused to have its name associated with it because of the sequence at the end when Watson takes over a ship and does some decidedly un-military maneuvers with it. The producers, desperate to receive the support of the Navy, came up with the idea of having Watson accidentally taking a sleeping potion and dreaming the entire sequence. When this scene was shot and edited in, the Navy lent its backing to the picture.