If you factor out drug use, the mentally ill population isn't more dangerous than anyone else.

I don't think that the media intentionally vilifies the mentally ill. Instead, I think that people in general seek mental illness as a partial explanation for extreme violent behavior. "He must be one sick fuck." It's much easier to explain human badness in terms of illness than to confront the more complex truths: (a) sometimes good or average people do bad things, and (b) some people are just horrible.

If you start concluding that all extremely violent people are mentally ill (which is probably false) and use the flawed (A -> B) -> (B -> A) thinking that passes for logic among many people, you start thinking of mentally ill people as all potentially violent.