Most domestic abusers are already denied gun ownership. As far as mentally impaired, if they are Court determined "impaired", they would be banned from gun ownership. Those mental cases just wandering around are a diffcult task to balance rights. I, too would like them to be restricted, but it takes a lot of effort to ban them legally. That's why people/family are asked to report a person with issues that wants to buy a gun.
It is a major problem, don't know if it can be solved since the mental one has rights too.