In Paul's Case, what exactly is wrong with Paul? Please explain as much as possible.

This is a debatable question, but there have been many
consistent arguments on what could be possibly wrong with him. I am going to go with the
theory that he is Narcissistic and that such is the disorder he
has.

Paul is disgusted at everyone, at people's bodies, at
the lower classes, looks down on everyone, and cannot make any realistic human
connection.

He sees himself as a Dandy who deserves
everything. He centers everything around himself and even the trouble he causes is
caused by his lack of interest in school and terrible relationship with his peers and
teachers. He is obviously unwilling to change, not even for the sake of his parents, and
his presence causes such anger among people that you can tell he is not a "normal" or
mentally healthy human being.

His narcissismand
self-absortion led him to commit robbery just to self-gratify with a trip to New York
and a stay at the Waldorf Astoria, to enact his Dandyism and fantasies against the norm,
and against the law.

Paul is seriously selfish, immature,
and fastidiously antisocial on the psychological side.  The fact that he committed
suicide puts him in the psychotic side as well. This why he fits the narcissistic bill
quite well.