This may just be me.  It may not actually be in the song.  Certainly, in a literal sense, the point-of-view is second person, from beginning to end.  But my experience, and what I suspect may have been so impactful, and enduring, to millions of other people, is that the tone, and the mood, and the point-of-view of the song seem to change.

At the beginning, the attitude is almost contemptuous.  “How does it feel?”  And, however it does feel, you deserve it.  Talking loud, and acting proud, and throwing dimes down at the homeless people around you.

But then a more third-person slightly objective type of a feeling seems to creep in.  There is still a “you” to whom the words are directed; Miss Lonely in particular.   But you start to feel like he (or you, if you are thinking or singing along) are more just describing the way things are.  Perhaps not quite empathetic; but not as contemptuous.

And then. finally, by the end of the song, the feeling is more first-person; first-person plural.  Cuz we are all just out on our own.  With no direction home.  Like a rolling stone.