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Soon after the end of World War II, Congressman Mandeville is looking for an excuse to deny the Navy its $4 billion in appropriations.  To that end, he seizes on the fact that a destroyer escort called the Kornblatt has gone missing, and orders Adm.  Philo Tecumsah Bludde to find it within ten days.  Bludde has his men bring in the lieutenant to whom the ship was last signed out, John Paul Steckler VII, a bumbling but loyal naval man who is at that moment leaving for his honeymoon with his bride, Prudence.

The MPs inform John that he is needed in Washington, and hoping that he is to be awarded a medal, John hurries there with Prudence.  John’s composure before a roomful of glaring officers causes them to suspect that he is a cold-blooded master criminal, but as soon as he discerns that he is wanted for stealing the Kornblatt, he collapses into his customary incompetence.  Bludde, sure that John is a double agent cleverly preparing an insanity plea, informs the lieutenant that he must scrutinize thousands of naval records in search of the missing ship.  John brings the records to his hotel room, where Prudence awaits with high hopes for her first night of marriage, and has almost succeeded in seducing him when the MPs arrive to sequester John in bachelors’ quarters.

In the morning, Bludde sends John to Naval Intelligence to meet with Ens.  Benson, and after John discovers that the ensign is a beautiful woman named Rita, his awkward attempts to be suave convince her that he is a dangerous spy.  She quickly hypnotizes John so he will relate his last days aboard the Kornblatt: As the war is declared over, John accidentally releases a depth charge, but when it brings to the surface a Japanese submarine, he is promoted to lieutenant.

When they reach Pearl Harbor, each officer turns over responsibility for the ship to his subordinate, until John, the lowest-ranking officer, is left in charge of returning the ship to San Diego.  With no experience in captaining a ship, John manages by surreptitiously reading from an instruction book, but when the book is blown overboard, he soon is lost at sea.  The ship founders into a reef, after which John and his chief boatswain, Stan Wychinski, motorboat to the nearest shore.  There, John falls over a cliff and, hanging on to a tree branch, calls for help.  Wychinski races to rescue him but by the time he arrives, John has been captured by Japanese soldiers and Wychinski assumes he has fallen over the cliff.  As Wychinski returns to the ship and sets sail, John is brought before Col.  Takashi, who is unaware that the war is over.  He sentences John to execution and tortures him by keeping him awake for days.

On the morning of the execution, John cannot stay awake, forcing Takashi to interrupt the proceedings.  Just then, the colonel receives word that the war is over, and has his entire battalion surrender to John.  After listening to John's story, Rita now believes that he is too ineffectual to have stolen the ship, and determines to locate Wychinski.  Just as John returns to Prudence, who awaits him in her lingerie, the MPs once again detain him, as Rita has found Wychinski in Miami.  They fly to Florida, where Wychinski works as a wrestler.  John questions him in the middle of a match, but the wrestler receives so many blows to the head that he cannot recall what happened to the ship.  A hurricane develops that forces John and Rita to return to Washington via train instead of plane, and when only one compartment is free, they are compelled to share a bedroom.  Rita is initially concerned that John will harass her, but is soon impressed by his innocence and love for Prudence.

When they reach Washington, however, Prudence and her mother have met the train and both assume the worst when they learn that John and Rita have shared a compartment.  Just then, Rita and John discover that Congressman Mandeville has ordered an early hearing, so they rush to the courtroom, where Bludde warns John not to appear flustered.  While John sweats and fidgets, Mandeville accuses him of being a spy and Rita of being a conspirator.  The situation seems desperate, but Wychinski is at that moment searching for Prudence, and upon finding her, declares that he now remembers that the Kornblatt was sunk at sea for use as target practice.  They receive a two-day adjournment, during which John and Wychinski sail out into the ocean and dive, hoping to locate the ship.  They find it, but upon attempting to remove a bell with the ship’s name on it as proof, a giant octopus embraces John.  They finally break free and, upon delivering the bell to the courtroom, prove their innocence.

When Bludde telephones his boss to explain, the chief informs him that it was Mandeville who originally ordered the Kornblatt to be sunken without proper authorization.  John uses the information to blackmail Mandeville into increasing the Navy's budget, winning Bludde’s approval.  That night, as John and Prudence’s honeymoon finally begins, they are distressed to hear the MPs at the door once again.  This time, however, the men post a “top secret” sign on the door and stand guard.