To me a lot has to do with other issues relating to personal freedom. If someone cannot grasp something as simple as the 2nd Amendment, I have a very hard time trusting them with much more complex issues. I find that using the Bill of Rights, especially the 1st and 2nd Amendment to be a good "litmus test" due to the simplicity and ease of understanding. Does that make any sense?
He's proved an ability to grasp complex issues through turning around New York City and also how he'd deal in an extreme crisis. Quite a long track record. Sure, he's been clearly wrong about some issues, but on the whole he's been quite good.