When the Nautilus is first sighted from the frigate Abraham Lincoln, it is declared to be "...30 degrees off the port bow." However, in the long shot that shows the approaching light, it is off the starboard bow.
The motto in the crest of the Nautilus reads "Mobilis in Mobile", and professor Aronnax translates it as "Free in Freedom". That is not remotely correct. Actually, the accurate Latin form (depicted also in the novel) is "Mobilis in MOBILI", and it means "moving in a ever changing environment".
When the sea monster attacks, the crew gathers in the library for a conference with Nemo. The ship is listing heavily, so much so that the actors have to hang on to things as they struggle across the room to reach Nemo. However, the water in the library's aquarium is tilted as well (revealing that the set is actually perfectly level, but the camera has been tilted to imply the ship's list).
After visiting Atlantis, the Nautilus surfaces. While the crewmembers are on deck, you can see the cables attached to the stars suspended in the sky.
Most of the books lining the shelves in Captain Nemo's library are Readers Digest condensed book collections. This is particularly evident in closer shots; no attempt is made to disguise the distinctive Readers Digest binding.
The "dive vests" worn by the actors are quite clearly modern SCUBA BCDs (buoyancy compensation devices). "Fastex" (side-release) type plastic buckles are seen at the shoulders; modern submersible pressure gauges and low-pressure inflator hoses dangle off to the left.
When the Nautilus hits the Scotia at the beginning of the film, the collision is strong enough to cause panic among the passengers, so much so that the Captain needs to intervene. However, when talking to professor Aronnax on the damages to the ship, admiral Sellings (staying true to the description in the book) says that collision was so light that the passengers did not notice anything until the sailors went on deck.