The ship shown as the USS Kornblatt was actually the USS Vammen (DE644). De-commissioned August 1st 1962. Sank February 18th. 1971, after being used as a training target for a Condor missile.
Not only was the USS Vammen DE644 (Destroyer Escort) used as the fictitious USS Kornblatt but so was her crew. The scenes (at around 37 mins) are the USS Vammen crew desperately trying to follow Jerry Lewis' delightfully chaotic commands.
Ensign Steckler and Chief Wychinski go to explore an island after their ship has run aground. While exploring the island, a background shot of the ship shows it rolling in the sea swells.