One problem I had was with my special ed son. He is very "young" even though he's grown. He mostly likes coupons and anime, and kid stuff, so I never worried about him and rarely checked.
Well, I noticed one day that he had a couple of men that he barely knew that were his new "friends". They were friends of friends of friends, or so the story goes. He really didn't know them. Well, they were engaging him (trying to set up a meet) that was disturbing to me. He was uncomfortable, too, so he did unfriend them and refused to answer. But I was surprised that he had allowed them in.
If a photo gets tagged, you can get it untagged, but if it has gone out to a bunch of people, I don't think you can get it back. So, someone can have a picture of you that you have no control over, and then tag it and send it to many.
Another time, and I think this was Yahoo and not FB, I was alerted that a friend of mine had commented at some blog. It even showed me her comment. I asked her if she knew about it and she said no. We both had to change our privacy settings (and the rest of our family's) to stop it. Again, I think that was Yahoo.
Someone out there probably knows more than me, but those were just a few of my experiences.