WOW to this thread.
I have my fb on the highest standards and am hopefully extremely unsearchable. But even if I were, there really shouldn't be anything on anyones fb account that could get you in trouble (but I'm not your mom so thats up to you).
But regarding facebooking clients - there was just an article on this in one of this years APAGS magazines. According to them, it is OK. But with an exception. You make two accounts, one being your personal one and another being your professional account. Your professional account lists your websites and is used as a resource for clients and others in the psych field - posting helpful links and worksheets and videos, etc. Kind of like a business profile, but for you. However, I would never personally want to be "friends" with any of my clients or customers at any of my previous jobs, but I guess I keep my privacy levels on high due to the population I work with.
About facebook friending supervisors, it depends on them. One of my supervisors I won't and another one added me and it took me about a year to accept it. Professors I have never felt the urge to do so, not sure why I would want to - maybe afterwards to keep in touch.
But yeah, i believe its personal preference as long as you are keeping strictly to the code of ethics and keeping everything professional.