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.
Paul in Cather's "Paul's Case" can be viewed in other ways, as well. The title suggests that Cather presents Paul as a case study, that she presents Paul as a case to study in psychological terms.
As such, Paul can be seen as suffering from major depression. Certainly today many psychologists believe that anyone who commits suicide by definition is suffering from major depression. Paul condemns almost everything. He takes his feelings about his own situation and transfers them outward. Everything is soured and ruined, and when his money runs out, he is left without hope.
Also, Paul in a sense is a frustrated artist. He is probably not in love with the art itself, though he does seem to admire paintings. More likely, he is in love with a certain lifestyle that art makes possible for artists. Note that his room in New York is not perfect until he has just the right touch--the flowers. He is almost like an interior decorator. He is in love with a lifestyle he cannot possibly maintain, and again when the money runs out, he would rather end his life than retreat to a life he refuses to go back to.