The submarine shown in stock footage was not the USS Nautilus (SSN-571). It was the USS Skate (SSN-578). The Skate was the second sub to reach the North Pole after the Nautilus accomplished this historic feat the previous week. The Nautilus is seen at the sub base, where as of 2018 she remains as part of the Submarine Force Library and Museum, being the world's first nuclear-powered submarine.
Long shot shows Parrish and Paige in a convertible with the top down, but when the closeups come, the top is up.
Lucy tells Parrish that tobacco poisoning is like poison ivy "only you only get it ONCE." In the next sentence she says "I sure was scared the FIRST time I got it."