Private police, though ... in an era where early death is relatively uncommon vs. omnipresent, what's their incentive to take risks beyond what they're paid for? That what can be problematic, there's many reasons self-help is outlawed, but in the examples you give there's no immediately obvious problem.
The customer of the privatized prison is not you but the state. As a result, they compete with each other to do the best "prisoning" (ie punishing bs rehabilitation, using them as almost-slave labor) for thirst cost. If you were the customer, (as in you directly picked your prison provider), the incentives would be much different: http://youtube.com/watch?v=SzYJYSm-MfI
The video presenter presumes people will follow rules --even violent people will follow rules --what force is going to enforce those rules 'not being on someone's property', for example. And unless all communities are run similarly, this will create 'outcasts'. Bad actors would just find another place to lay low.