Ah, the hardest part of a Whitman poem: figuring out just who's doing the talking. Who is this "I" who claims to be watching us like a ghost? The speaker tries to identify with everything in the world, to the point that he seems to want to contain everything, or at least reflect it like a mirror. He compares people to actors and says that the body is the key to understanding one's identity. In "Crossing Brooklyn Ferry," we're all just containers of marvelous solids and fluids.
The speaker of the poem has no independent self. He's just a mirror of the world around him.