What about a national database of future criminals?

One aspect of the gun control debate that's been getting a lot of discussion is that of a mental health background check of gun customers. The NRA, for one, is pushing this idea.

Setting aside the question of whether the Supreme Court would ever countenance taking a right away from people based on speculation that they might commit a mass shooting, would that entire way of thinking be a slippery slope? After all, far more people are killed in speed-related auto accidents than in mass shootings, so the logic behind trying to predict who might misuse a gun and then taking their gun away before they've even commited a crime would seem to apply just as well to predicting who might drive over the speed limit. If we did that, we could save far more lives. 

There's a TV show called Person of Interest. The idea is similar to that of Minority Report: predicting crimes and stopping the criminals before they've even done anything.

Is this a road we want to—or should—go down, even if it were effective?