S.H.
My daughter isn't old enough for Facebook or anything yet (she's 4 lol) But I use Facebook myself. I just wanted to point out that you may want to have children clean out their Applications regularly.
Mouse-over "Settings" at the top right of Facebook, then click Application Settings. It will give you a list of Recently Used applications. These are everything from games to those silly quizzes! If they are not actively using an application, they should click the X beside it to remove it. Those applications have access to your information on your profile, and there's no sense in them keeping that access if you are not using the application!
From that page you can also change the list to "Authorized" and other options to clear out more. You change this using the drop down at the top right of the list where it says "Show".
Remind them that they should read things before they click on them, and before clicking "Allow". Be careful with contests that have fine print. They can be confusing and end up leading you to buy something!
If my daughter was old enough for Facebook, I think I would probably require her to set the privacy settings to only allow her friends to view anything. Might bump it to "friends of friends" if she were in high school lol
Hope that helps!