Well, in my state if you have any sort of stint in a inpatient mental health facility you can not purchase. If you have any sort of violent misdemeanor (even simple assault), you can not purchase. And I think, think, if you have been dishonorably discharged from the military you can not purchase. At least not legally.
Here's the thing. What is regulation? A law, right? Bad people, or criminals, by definition to not obey laws. That's why they are considered criminals. If you regulate guns until you are blue in the face, all you are going to do is prevent good law abiding people from having guns. The criminals and those with ill intent will have them, leaving the innocent vulnerable and easy prey by the predators of society.