The world's first nuclear-powered submarine, which would become the first submarine to transit the North Pole while submerged, also bore the name Nautilus. While it wasn't the first ship in the U.S. Navy to bear the name, the choice probably wasn't entirely coincidental.
The inventor of the first truly functional submarine, Simon Lake, was caught in a storm, and recalled a moment in Twenty Thousand Leagues Under the Sea where the Nautilus dives a few feet underwater to avoid the storm. He then repeated the technique and survived, and sent Verne's great grandson a telegraph thanking him.
The book is famous for also inspiring Ernest Shackleton, William Beebe, Robert Ballard and Jacques Costeau.
The North Pole is placed in the Arctic Ocean. The South Pole is placed in Antartica, a sheet of ice thousands of feet thick, and most of it on a solid continent. The Nautilus could have reached the North Polenote and indeed, the USS Nautilus (America's first nuclear sub and namesake of the vessel in this book) did reach the Pole by travelling under the Arctic Ocean, but not the South Pole.
The Nautilus was supposed to make 50 knots on Bunsen batteries. The only modern submarine which could approach 50 knots needed 30 000 kW for the main engine. To get 30 000 kW from Bunsen cells their combined size would exceed Nautilus entire hull in size by a few orders of magnitude.
Also, an in-universe example of Schizo Tech: despite the usual rotating electric motor with brushes being known and used in the 1860s, Nautilus main engine is an oscillating electric motor ( "where large electromagnets actuate a system of levers and gears that transmit the power to the propeller shaft") - less efficient and a royal waste of space.
The new technology of double hull seemed to solve most problems in an age when most vessels were still wooden sailing ships, so Verne become enthusiastic about Nautilus double hull able to withstand the pressure "in the deepest ocean trench". No double hulled submarine can go below 1300 meters, specialized deep-diving vehicles are small craft with 5-inch thick shells.
The Nautilus' primary armament being a ram was typical of naval thinking at the time: this was right after Monitor versus Merrimack, and it was thought that since ironclads could not hurt each other with cannon fire, the only option would be ramming one another. At this point breech-loading heavy guns were new and untested, nobody had yet worked out how to fire a high-explosive, high-velocity shell without blowing it up, and nobody had fired a self-propelled torpedo in combat. It would not be until World War I that the submarine's role as a torpedo-carrier was cemented.
Nautilus crew diving suits are an autonomous version of the heavy helmet of Verne's lifetime, yet all these had been used only to very shallow depths. To use them hundreds of yards deep with no decompression stops would only make the divers succumb to decompression sickness. Illustrations, including the original's, however, show them as having air tanks rather than tubes that could break.
Channel Hop: Originally a 20th Century Fox project, Fox studio manager Sid Rogell personally sold the film rights to Walt Disney, who apparently returned the favor by having some scenes filmed on Fox's backlot.
Throw It In!: When filming the scene where Ned and Conseil get in the boat to row away from the cannibals, Kirk Douglas expected the boat to be low in the water. He didn't lower the oars far enough to catch the water, and when he started to row, he fell on his back. Director Richard Fleischer thought the shot was so funny he left it in the film. When Ned starts to row, he clearly tips back, and his legs shoot up in the air.
Wag the Director: The scene at the beginning of the film where Ned Land strolls up with a beautiful girl on each arm to the lecturing sailor and the ensuing fight was added at the suggestion of Kirk Douglas, who wanted to preserve his image as a macho action lead.
Walt Disney originally considered making this film as an animated feature; the detailed pre-production sketches by artist Harper Goff, as well as Goff's enthusiastic suggestion that it be done as live action feature, convinced him otherwise.
The first tests for the final battle took place against a beautiful sunset, on a calm sea. The first Giant Squid had stuffed tentacles held up on wires; these grew heavy and hard to control as they took on water, and the bright sunset made the wires painfully obvious. Disney himself was appalled at this first footage, and demanded a reshoot. This reshoot nearly forced the studio out of business, but proved worthwhile when the film earned a nomination for Best Visual Effects at the Academy Awards.