There are some felonies that should cause you to lose your gun rights, but others that shouldn't, same with mental illness. I think you should be a citizen before being allowed a gun (or be required to take a class to assure knowledge and conformance with laws). Other than that (and a handful of other minor things) I think guns should be allowed by anyone (18+), in any condition, anywhere.
I feel anywhere (including Wal-Mart, etc, etc) that takes measures to assure our safety (metal detectors, armed guards, secure gates/doors, etc... Like airport, courts, jails, etc currently have) and can restrict guns (but it must be REAL protection, not the fake pat downs like they do at the E-center), but anywhere else should be required to accept guns. They should also be required to assume ALL responsibility for your safety while in there "secure" locations (including all financial responsibility for lawyers and a $10 million insurance for each person while on site) and provide lockboxes for your gear. If they do all that then they can ban guns.
I think employers can ban guns unless you take a class (private or government, I don’t care) to assure proper gun handling/knowledge, but if you pass the class then you can carry there too (just like operating a fork lift, etc).
Bad Guys don’t obey the law, so any laws in place need to be to help the good guys, not restrict the good guys.