People always like to run down cops for not being able to shoot. I will admit that most of the cops I work with don't shoot as well as I would like them to, and that goes for almost every department I worked for.
However, I've taken a couple of CCW classes that involved live fire. In my experience the average CHP applicant is a worse shot than the average cop.
That said, in my experience, the average private security guard or corrections officer is a worse shot than the average CHP applicant.
In general, my experience has been that people who carry guns, professionally or otherwise, can't shoot as well as they should be albe to. There are, of course, exceptions in every category.
The problem is that if we make the tests and qualifications hard enough that only people who really know what they are doing can pass, we start denying people their rights. Its really a no win situation.