The nuclear-powered 'Hydronaut' was actually built as the 'Submanaut' in 1956. It was originally a working scientific submersible whose primary function was to inspect underwater pipelines, but was diesel-powered and carried only two crew members. It could also not circumnavigate the world. Later in the 1960s, it was used to shoot underwater films for various movie companies and TV productions in the clear waters off Florida and The Bahamas. Initially built by Martine's Diving Bells of San Diego California at a cost of $1.5 million, it was purchased in the early 1980s by Six Flags for $500,000 to be displayed at its Atlantis water park in Dania, FL and then by nearby Grand Prix Race-O-Rama for only $12,500 in October 1992. Sadly the Submanaut was cut up on-site and sold as scrap in the early 2000s.
When Dr. Volker (David McCallum) is setting up the radio signal near the end of the movie the noise it emits is the same as the communicators from The Man from U.N.C.L.E, which also starred McCallum.
The all-white ship that is seen at the beginning of the film is the USCGC Diligence (WMEC-616), a Reliance-class United States Coast Guard 210-foot Medium Endurance Cutter. She was commissioned in 1964, and began her service at the Key West Coast Guard Station (also seen in this film). The 'Dilly' is still in Active Service as of this writing (Mar 2020), and has lived up to her name receiving countless honors including numerous service commendations, medals, and special operations ribbons during her 55 plus years of service.
The colony of small, stalked plants that Hank finds in the sand and from which he collects a sample is Penicillus, which goes by the common name of Merman's Shaving Brush, Neptune's Shaving Brush or Shaving Brush Plant. It's a type of green algae commonly found in the shallows of the Caribbean.