That we're all serial killers. ASPD isn't going to make you a serial killer more than anyone other personality disorder. Also, that we're all abusers and can't be trusted.
Honestly there isn't that many accurate stereotypes about people with ASPD. It's been so demonised in the media and pop psychology. The Idea people get of ASPD usually comes from sensationalist movies or TV shows.
A common example is Patrick Bateman from 'American Psycho'. From what I've seen Bateman is obsessed with how he's seen by others and is prone to having power fantasies. He seems more NPD to me. I don't really care how I look anymore then any other woman does.