Why Aren't Autistic People Psychopaths?
Many of the major theories about psychopathy, if accurate, would predict that autistics should have psychopathic traits.
Take Blair's Violence Inhibition Mechanism (VIM) theory. Drawing an analogy to animals who have certain nonverbal cues of 'surrender' (eg a dog lying flat against the ground with ears back and whimpering), this theory suggests that most individuals are hardwired to suppress aggressive behavior in response to distress cues (fear and sadness). Over time, through learning, this gets extended into a moral code in which behavior that harms others is forbidden. This leads to the moral-conventional distinction seen in virtually all non-psychopaths, in which harm-causing violations (but not social convention violations) are described as wrong regardless of what authority figures say or what norms exist in society. Since psychopaths have difficulty recognizing fear and sadness, and distress cues don't elicit negative affect in them, this connection doesn't get made and the basic foundation of morality is absent.
Problem is, autistics are also poor at recognizing fear and sadness (along with every other emotion, of course). Even though distress cues elicit negative affect in autistics (Blair ), in everyday life autistics will effectively see these cues a lot less often and a lot more inconsistently than neurotypicals do. The connection between their own actions and this sympathy-induced negative affect should be less strong in autistics, resulting in a weaker moral-conventional distinction and more real-life antisocial behavior. However, autistic people score completely normally on the moral-conventional distinction and aren't any more likely to engage in criminal behavior.
Another thread of research comes up with a similar problem. Dadds et al (2006) found that telling psychopathic children to look at the person's eyes eliminated their difficulties in recognizing fear, and in a later study they confirmed that psychopaths pay less attention to people's eyes when trying to recognize emotions (though Rime et al  found that psychopaths made more eye contact when talking with an interviewer, so this may be a situation-specific phenomenon). They suggest that lack of eye gaze could interfere with attachment in early childhood and have a cascading effect on the child's emotional development. Indeed, Frodi et al (2001) found that offenders, regardless of psychopathy, showed extremely low rates of secure attachment. In particular the dismissing style, in which the individual doesn't seem to think attachment is important, was very common. Cause and effect can't be established based on this, but it is supportive.
In contrast, although autistic kids do show lower rates of attachment security, this appears to be mostly due to parental reactions to having a disabled child. In particular, it shows no relationship to autistic social symptoms, and many autistic kids show clear evidence of secure attachment. In particular, many autistic kids who avoid eye contact show secure attachment, despite making far less eye contact than psychopaths do.
So, the fact that autism and psychopathy are clearly distinct conditions means that researchers, when trying to explain psychopathy, should avoid explanations that apply to autism as well. Specifically, they should ask the question - what's different between autism and psychopathy?
With regards to the moral conventional distinction, it's interesting to note Leslie et al (2006)'s study, in which autistic and NT children were asked to evaluate, along with standard moral-conventional vignettes, a vignette involving a 'crybaby'. Specifically, James & Tammy have both been given cookies, and James wants to eat Tammy's cookie as well as his own. Tammy eats her cookie, and James starts to cry. Both autistic and NT children agreed that Tammy hadn't done anything wrong, even though her actions made James cry. This indicates that mere distress cues are not enough to explain the moral-conventional distinction.
So, what does underly the moral-conventional distinction? Is it a sense of fairness? Even many animals show a sense of fairness, and fairness is obviously relevant to moral concerns. Maybe the moral-conventional distinction works on the 'golden rule' - the child can imagine not wanting others to engage in moral transgressions even if they weren't forbidden, whereas their only objection to social conventional transgressions is when someone else gets to do it while they can't. It would be interesting to study the sense of fairness in psychopaths. The only study that has directly examined this did find that psychopaths had less concern for equality than non-psychopaths.