Background Checks for Gun-buyers

Some in our national government and some in various state and local governments are promoting background checks for gun buyers. The stated intent is to reduce violent crimes.

Removing guns from the hands of potential thieves, kidnappers, extortionists, rapists and murderers sounds like a good idea - a really good idea.
But who are these people? Who gets listed in the nation-wide "can't buy a gun" database? How do we know who should not have a gun?
Are they people who have been convicted of violent crimes in the past? Are they people with mental illness? Are they certain races or classes of people shown to have a high incidence of gun crimes?
Who are they and who gets to identify them?

If they are people who have been convicted of such crimes in the past and those people have spent the prescribed time in a correctional system, doesn't that simply and boldly say that our correctional system doesn't work. Perhaps that needs to be examined. Are we allowing uncorrected, potentially dangerous people to mingle freely with everyone else? If those people who had gone through the system were actually rehabilitated, why would we need to continue to penalize them by including them in a "can't buy a gun" database?

If people with mental illnesses are to be put in the "can't buy a gun" database, then which mental illnesses are they? Who gets to decide when an individual's illness is serious enough to qualify? What criteria are used to make the decision?
I am of the impression that there is quite a lot of variation among mental health practitioners regarding such matters. Such variation suggests there would be considerable inaccuracy in diagnosing the people in question. Inaccuracy can put people in the database who shouldn't be there and leave people out who should be included. That sounds like a very troublesome and dangerous situation.

If the people to be included in the database are of certain races or classes who have demonstrated a high incidence of gun related crimes, the problems devolving from that are so many and so great that no such criterion could never be used.

A "background check" of a potential gun-buyer would mean a check against the database. If their name shows up in the "check", the gun-buyer would not be able to complete the transaction and buy the gun they were shopping for. What then? Do they get a visit from some official? Or is the fact they are "shopping" simply ignored?

Such a database may sound like a good idea. But that's just it - it sounds like one. It would be too inaccurate and I suspect it would cause more problems than it would solve.

What else could such a database be used for? Perhaps it could be used to restrict alcoholics from buying alcohol - or over-eaters from buying too much food... many, many other uses can be imagined.