Most of the ridiculous things I've heard weren't about me specifically but my disorder in general, as I don't often tell people that I'm a psychopath. Some of those things include...

Psychopaths have black eyes. I have blue eyes.
Psychopaths have empty eyes. If I had empty eyes, I wouldn't be able to see.
Psychopaths are demonically possessed. Then find me an exorcist.
Psychopaths are demons in the flesh. So that explains why holy water makes me itch...
Psychopaths are lizard people ("reptilians"): http://stargods.org/ReptilianStare.htm -- Quote from the site: "The bottom line is that no difference that can be found between a Reptilian and a Psychopath. The occult label for these people is Reptilian and the psychiatric term is Psychopathic. If some one you know gives you this look, then it is best to avoid them. More examples below. These people may or may not be reptilians, but are offered as possible examples of what the "stare" looks like. It is an empty hypnotic look."...Seriously?
Psychopaths eat people. On the contrary, most cannibalistic serial killers were not psychopathic. See: Dahmer, Chase, Fish, etcetera. And still, I hear this one all the time...
Psychopaths are emotional vampires (purported by experts). I want to suck your love.
Psychopaths are real vampires.

If you have any more, please let me know. I'm going to make a list...

*Edit*
Psychopaths are psychotic. Just... No...
Psychopaths are serial killers.
Psychopaths are not human/subhuman/monsters/etcetera (also purported by experts).

John Clarke, the author of this drivel, has a PhD in psychology.