Other mistake: In the scene when the League are attacking the factory, we see Captain Nemo demonstrating his skill with his sabre. In the last shot before the scene changes, he cuts down a number of people and then sheathes his sword all in one movement. The camera angle is from the side where his scabbard is hung, and although you can hear the hissing sound of the blade being sheathed you can see the sword completely misses the scabbard and is just stuck out behind him. This is obvious because the sword is silver and the scabbard is black.
Other mistake: In the scene right after the team gets a Morse code message from Skinner, we see the holes made in the Nautilus. The one in the middle is smoking whereas the one in the back is not. If the ship was filling with water to the point that is was immersed due to the holes then whatever explosive components would be wet and extinguished. So by the time the Nautilus resurfaced, it should not have been smoking at all.