Factual error: It is barely credible that a young Victorian woman like Elena would even think about wearing a goatskin miniskirt - exposing her legs in those days would be akin to walking about topless nowadays. Even if she did those bright yellow cotton knickers - gleefully visible in the scene in the beehive - are in no way from the 1860s. Her pants are a hundred years ahead of their time.
Factual error: The Confederate Army did not take black Union soldiers as prisoners. Those unlucky enough to be captured would be taken back into slavery or, far more likely, simply killed on the spot.
Factual error: Captain Nemo takes the castaways on an underwater tour around the island, where they observe Greek temple ruins on the sea floor. The ancient Greeks were pioneers of philosophy, politics and engineering, but they never colonized beyond the general area of the Mediterranean and they certainly never colonized the South Pacific (which is the setting of Mysterious Island).
Factual error: All low pressure storm systems generally end up traveling from west to east in the northern hemisphere. So soon after take-off the balloon would have been over the Atlantic Ocean for the next several days. Europe would have been the next large land mass seen.
Factual error: At the beginning of the movie they are flying in the balloon for several days. The wind is constantly blowing everything around, hair, clothes etc. I've been in a balloon. Since the wind is blowing the balloon, you are moving at the same speed as the wind, therefore, you don't feel any breeze or wind, it's dead calm.
Factual error: The balloon that the Union soldiers escape in has no mechanical burner of any type in it that would be needed to keep the craft aloft in the air. A balloon flies by heating the air inside the bag, causing it to rise up. It descend as it cools.
Suggested correction: Gas balloons (using Hydrogen or Helium) large enough to carry passengers were invented in the late 1700s. Gas-filled observation balloons (such as the one in this film) were, in fact, used during the Civil War.
