I had meant to make a similar post to Janet's but it seems it didn't go through. Basically what she said. I do not feel comfortable sharing other people's stories online, especially those I'm not in touch with any more, but my experience has always been the biggest factor in not seeking or accepting help for mental illness has been cultural and social baggage. Even if that is sometimes enhanced by the illness it tends to come back to the cultural perception of being mentally ill rather than inherent to the disease.
But this one I'm a little 50/50 on. I've never really had a problem with shows making fun of autism, OCD, etc. But then again I tend to view dark humour as a kind of coping mechanism for dealing with the more depressing stuff this world has to offer. I've generally got no problem with people making fun of serious issues, as long as they keep in mind that it's a serious issue.
The problem comes when dark humour and other problematic, stereotypical depictions ("all schizophrenics are violent killers", "depression is something you can just snap out of", etc) are dominant in popular culture. You might get sensitive, realistic depictions of mental illness in the occasional independent film or even rarer documentary. But the vast majority of popular culture goes for the cheap laugh or the harmful stereotype, perpetuating them, ingraining them deeper into the social perception.
If there was enough visible and prominent outreach being done to change the dominant stereotypes (there are plenty of activists but rarely visibility outside the community),
if there were cultural awareness of the realities of these illnesses beyond the stereotypes,
then I wouldn't have a problem with the dark humour. I truly don't have a problem coming from shows that have good, non-problematic depictions injecting humour into them; that's actually a damned good thing and part of making the depictions well rounded and realistic
*. But we aren't there yet.
On the gun control side, I still don't believe there is a realistic path to legally denying the mentally ill guns that doesn't make matters worse. On the practical side you have information sharing and enforcement issues. On the cultural side you are further demonising mental illness and discouraging people from seeking treatment. Again, most of the potential issues can be better addressed by working to improve mental health care and removing the barriers to treatment. Including (especially) the cultural ones.
I was trying to think of an example and came up with Toph from Avatar and the humour around her being blind. I realised later that this is a good example of general disability but not mental illness which was at point. I usually discuss these issues in terms of marginalised groups in general or ableism as a whole, accounting for both physical and mental disabilities.
The fact that this was the first example I jumped to (and easily the strongest I've been able to think of) probably says something about both me and pop culture, but I don't want to dwell on this.