The right to "freedom of speech, freedom of the press, freedom of religion, freedom from self incrimination, right to privacy, right to not have to shelter troops against ones wishes, right to a trial, right to not being subject to cruel and unusual punishment, the right to not have a established government religion, AND the right to defend oneself" are unalienable rights endowed by the Creator to all mankind.
These right enumerated in the first ten amendments to the Constitution of the United States are rights that are either understood as "negative or positive" rights. They are either rights that the government CANNOT take away from the citizenry without just cause or positive rights that the people have.
Good, bad or indifferent... The criminals are not going to "play by or abide by" the laws on the books. Look at Mexico where its illegal for their people to own guns. Yet tens of thousands have died yearly down there for the past decade. Why?? The cartels are NOT obeying their strictest gun laws that they can have.
Should mentally unstable people not own firearms?? Yes I agree with that. How to implement this into a practical law that doesn't violate the right to privacy from the government is a huge sticking point. But I do believe it is something to be worked on and out. Now do I believe EVERYONE who desires in getting a firearm be subject to mental health testing?? No. The criminals certainly will not be subject to this nor will blood thirsty terrorists.
Firearms are often a symptom of a FAR larger problem. Just look at Cuidad Juarez for that obvious answer. It's the drug trade that's the major root cause in the firearm deaths in Mexico and the US. We already have MANY gun laws on the books here. I'm not against more necessarily however, I want any new laws to have A REAL purpose and have some efficacy in at least keeping criminals from legally buying guns.
Remember that crazy guy who killed over 70 and wounded over 100 teenaged people in Europe?? They had very strict gun laws there. So does France. So does Chicago Illinois too. Criminals bent on evil will not be kept at bay with feel good laws. Far more to this puzzle then just that.