I don't think a psychiatrist would say mentally ill people are dangerous--that's
a stigma popular entertainment creates. Most dangerous people are sane. People
who are mentally ill may seek treatment or have to have treatment because they're
a danger to themself or others. Most as schizophrenic as you describe show
secondary symptoms so most people, at least, would notice and report it to some-
one.
The notable experience I've had recently of noticing that someone was obviously
mentally ill and dangerous but wasn't recognized as such by many was when I read
the posts under some YouTube clips of Charles Manson. He actually has a lot of
defensive fans who think he's a misunderstood and mistreated brilliant man (?!).
http://www.trutv.com/library/crime/serial_killers/notorious/manson/murder_1.html
http://en.wikipedia.org/wiki/Charles_Manson