Before proceeding to the title of this post, I need to make some disclaimers. I have no training in psychology and have never met Arenas. Only a qualified psychologist or psychiatrist can actually make a diagnosis. All I can do is observe symptoms and form hypotheses. Even the symptoms I observe are hearsay, based on what I have read. If I make a mistake anywhere, my hypothesis falls apart.
When I read of Arenas' behavior, I originally thought he was just another narcissistic athlete. Upon reading about the incident, several details make me suspect that he has Borderline Personality Disorder, possibly with traits of or in combination with Antisocial Personality Disorder.
Gilbert Arenas allegedly got into a dispute with his teammate, Javaris Crittendon, and brought 4 unloaded guns to the Wizards' locker room Verizon Center with a sign "Pick One." Crittendon drew his own gun and chambered a round. (source) This could have been a low-risk suicide attempt (DSM-IV criterion #5: recurrent suicidal behavior, gestures, threats or self-injuring behavior). According to Sally Quinn, he is "a man with sharply veering moods, whose sense of self is highly unstable. These match criteria 6 and 3, respectively, affective instablity and identity disturbance. According to Colbert King, Arenas has "three children with his on- and off-again girlfriend." This matches criterion 2: A pattern of unstable and intense interpersonal relationships. Thus, we have evidence for 4 symptoms of BPD, 5 are needed for a diagnosis.
As for the Antisocial Personality Disorder, Arenas' increasingly boorish pranks may show a disregard for other's safety (criterion A.5). He lacks remorse, as evidenced by the "joking" gunplay pantomime (criterion A.7). He was very charming as a child. APD often produces superficial charm. The other criteria and characteristic behaviors are very hard to judge at a distance.
So, what should be done about Arenas? It's better for him to be treated than to be in a prison cell. (This is also true of far too many convicts.) So, the law should force him to have a mental health evaluation and give him a suspended sentence to enforce his treatment. The NBA should ban him for life, with the ability to apply for reinstatement. The last may very well be the strongest incentive.