Would you check your employee's facebook page or take action for it content?

No, would not unless, the employee is not performing well, even after being made aware. The social network is still public, even if it claims other wise. I don't take compromising photos of myself and snail-mail them as greeting cards to my friends. So, if I happen to see something distasteful by my employee, that will have an affect on how I see them. I would make it known if it was not good for business.