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First off, if someone has NO criminal record, then how would YOU suggest they "scrutinize" people? What information is it that you are looking for before you "allow" a person to practice his/her constitutional rights?
Perhaps you are advocating for MORE government interference to actually invade our privacy as well?
The Second Amdendment is about Militias. Now, I was a member of one of them thar "Well-Regulated Militias", and before they let me have a gun, they fingerprinted me, put me through weeks and weeks of training and then only let me fire the gun under controlled circumstances until they were sure I knew what i as doing.
But going back to my point. Everyone in the life of Cho/Loughner/Lanza knew he was nuts, and we find this out usually before they've bagged up all the bodies. I don't think the Founding Slave Rapists had them in mind.