In at least two roles, the casting could not be improved. Kirk Douglas is perfect as the harpooner Ned Land, a boisterous sailor (and hero) who will not bend to any authority. Douglas plays his character with his usual relish, and even redeems himself well while singing "A Whale of a Tale", the movie's signature song.
James Mason is also quite comfortable as Captain Nemo, the soft-spoken but misguided genius behind the Nautilus. Set in the late 1860s, Nemo has decided to fight mankind's wars by joining them, and sinking armed vessels of all flags. His crew is completely devoted to him, partly because he's freed them from slavery or some such thing, and partly because it simplifies the plot.
There's plenty of action to savor, as well. Ships get blown up, cannibals are on the hunt, and a giant squid for whatever reason decided to attack the Nautilus. The latter sequence is the film's highlight, certainly more so than the moralizing between Nemo and Professor Aronnax (Paul Lukas), who is something of a milquetoast.
The suspense of the squid battle is reduced somewhat by the fake rubber tentacles, and the inevitability that Land will be the one to vanquish it.
Peter Lorre, one of my favorite character actors of the 1940s, is a bit disappointing. By now clearly overweight, he gets plenty of screen time, but has little to do. Mostly, he follows Aronnax or Land around. He looks tired, and seems to be going through the motions.