Wait though Vermi... Wont the people with mental illness/history of violence just use another means to kill instead? Should we restrict the mentally ill from possessing knives and pressure cookers??
Even IF you restrict the mentally ill/individuals with a history of violence from purchasing guns, won't they just go through the burgeoning black market to buy guns? Drugs are illegal, but I can go buy a gram of heroin right now if I wanted.
Your ideas sound like a big-government bureaucratic nightmares if you ask me.