Is Leggatt real or is he another half of the Captain himself?
Strong arguments can be made for both sides. No one else sees Leggatt, so the white figure in the water that is naked as a newly-formed human would be is "born" as the captain pulls him from the water. Gazing into the dark waters, the captain may have psychologically realized that he has a dark side and, for a time communicated with it. (At one point in the novella, the pronoun "it" is used to refer to Leggatt, in fact.) Then, he has again hidden this darker side by resubmerging it in the depths from which it came. On the other hand, Leggatt may, indeed, be the first mate of the Sephora, whom the captain saves and hides in his cabin because he sees something in him, and because he is solitary. But, fear of the consequences of harboring a murderer may cause the captain to send Leggatt back to the sea.
Leggatt is a real person, and distinct from the captain. The story is about how Leggatt, a man without conscience, corrupts the (basically good, but naive and inexperienced) captain to the point that he endangers the whole ship. See Robert Hare's book Without Conscience for a description of psychopathy. What's amazing to me is how clearly Conrad can delineate this type of personality disorder.