mentally ill people are more likely to be stupid or dangerous
False on the dangerous aspect. Can you cite a source on intelligence? Obviously since "mentally ill" technically includes ANYONE below IQ 80, it's going to be lopsided, but I've never seen any research that suggests depression, OCD, etc. correlate with a lower IQ.
I had heard that contrary to some stereotypes, autism and schizophrenia are not associated with higher intelligence; and a bit of checking on Google Scholar seems to confirm that mental disorders are usually associated with lower intelligence:
http://archpsyc.jamanetwork.com/article.aspx?articleid=481989#qundefined :
There was no association between premorbid IQ score and risk of bipolar disorder. Lower IQ was associated with increased risk of schizophrenia, severe depression, and other nonaffective psychoses.
Here is a new post at EconLog in which Bryan Caplan discusses how signalling contributes to the status quo bias.