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.
Continuity mistake: When the two men are carrying water up to their new cave home (via a home made elevator), one of the men is holding two buckets of water. In the shot where you can see the sea behind them, this man hands the second man a bucket of water, which he takes. In the very next shot, from inside the cave, the first man has both buckets and again hands the other man the bucket of water. (00:48:35)
Visible crew/equipment: When the five men are going up the mountain, a crew member is seen beside a big rock, at the bottom left of the screen. (00:33:50)
Continuity mistake: As they are approaching the island, they have to climb into the ring above the balloon and cut the basket loose. It switches back and forth from long shots to close shots. In the long shots, the ring is at sea level bouncing off the waves. In the close shots, they are 10-15 feet above the water and some of them jump into the ocean.
Continuity mistake: After they've been on the island for awhile, Neb finds a chest floating in the water. It's about 6 feet long, made only of light colored wood and has two wooden bands around it. When Neb pulls it to shore it's a completely different chest. Now it's shorter, made of reddish colored wood and has iron fittings.
Visible crew/equipment: As the 5 men are climbing to the top of the volcano, there are several long shots of them crossing large rock formations. In one shot, they are still climbing while in the bottom left-hand corner a shirtless film crew member appears, seemingly unconcerned that the camera is rolling.
Continuity mistake: When Herbert and Elena are being walled up in the honeycomb, the shots showing both people and the entrance show them leaning against the side wall. The shots showing them from the front show them leaning against the back wall. This is repeated every time the shot switches back and forth.
Revealing mistake: When the castaways discover two women and a man washed up on the beach, they quickly determine that the women are still alive. The journalist, Gideon Spilitt, checks the pulse of the male and pronounces him dead; but the dead man's limp left hand very noticeably and unnaturally jerks twice just as Spilitt releases his wrist. The actor playing the dead man obviously had an anticipatory reflex action, but they chose to keep the shot in the film, anyway.
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: 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: 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.