In my opinion, absolutely definitely positively without a doubt to not let anyone who you work with - especially supervisors - have full access to seeing everything on your facebook. You never know when you'll get tired and post something that someone takes the wrong way or something worse. Just start a limited profile setting and dump anyone and everyone you work with (even people who aren't supervisors) into that category, and set it so they can't see anything other than your basic work/school/networks/etc information. One year while I was home for the holidays and had time on my hands I even went as far as starting a "limited profile" group and a "semi limited profile group." The first can only see the basic work/school/networks/etc information, and the second can see most of my stuff but never my statuses unless I specifically change that for a particular status message.

That's just my $0.02. Even though I am very careful about what I put on fb, I'm extremely paranoid about letting people see everything, especially if it is someone who I don't know extremely well or someone I work with or a professor. I feel like declining their "friend invite" or whatever it's called looks as though I'm trying to hide something, but accepting it opens up way too much sometimes. I got on fb back when it was just college friends. I kinda wish it could still be that way... But I guess even facebook had to grow up, didn't it. haha.