As noted in my answer to another question, psychopathy is a term that refers to a clinical construct describing a more aggressive and highly narcissistic form of antisocial personality. Thus, only a fraction of all persons with antisocial personality disorder will be considered a psychopath.
Regarding all serial killers being mentally ill, this depends on what definition of mental illness you use. In the eyes of the law, psychopathy and antisocial personality disorder typically do not qualify as a mental illness for the purpose a mental health defense, such as the insanity defense. This is because, to the best of our current understanding, these "disorders" do not rob the individual of their connection with reality. On the other hand, if we step away from the law and courts for a moment, can we say that persons with psychopathy have some type of "illness"? This is the subject of intense debate. Some believe that there is nothing "wrong" with them in the manner of a deficit or impairment that therapy can "fix." Instead, they exhibit an evolutionarily viable life strategy that involves lying, cheating and manipulating others. Another camp believes that psychopaths do have "hard-wired" brain abnormalities, and that we may, in the future, find that these abnormalities cause them to process emotions and think differently from non-psychopaths. But then the question remains: Can you call it an "illness" in the traditional medical sense? At the present time, most mental health professionals are very hesitant to view it as an illness in this sense.
[i] Langevin R. A Study of the Psychosexual Characteristics of Sex Killers: Can We Identify Them Before It Is Too Late? Int Journal Offender Therapy and Comp Criminology 2003 47(4): 366-382.
DERIL, Salt Lake City, Utah: Recently on TV I watched a report on research that suggested that a certain part of the brain, having to do with conscience, is smaller in psychopaths. Could this be the problem?
KNOLL: Yes, the show you saw was probably referring to a brain structure known as the amygdala, which we believe is responsible for processing emotions. In addition, other brain studies have suggested that psychopaths may have other brain abnormalities as well.
For example, some of the more commonly cited deficits found in psychopaths include abnormal language processing, amygdala dysfunction and impaired emotional responses. The common clinical observations of attenuated emotional and fear response in psychopaths have undergone preliminary investigation by functional magnetic resonance imaging (brain scanning). Whereas healthy controls showed enhanced activation of the emotion processing circuit in response to fear and emotion arousing stimuli, psychopaths displayed no significant activity in this circuit. These findings have led researchers to conclude that emotional and cognitive processing of aversive stimuli may occur via different neural routes in psychopaths. To extend the speculation, psychopaths may process fear and emotions in a "cerebral" (cool, calculating), as opposed to a limbic (emotional) manner. It is also important to note that the lifestyle of some psychopathic persons may involve either substance misuse and/or head trauma, both of which may further influence any underlying neurobiological impairments.
DERIL, Salt Lake City, Utah: Can one be a psychopath without being a killer?