As has been said, report them. Facebook has a strong whatchamacallit against bullying. Also, block and/or ignore them; not overly important, in the grand scheme of things, although it might not feel like it.

Real threats should always be reported, technically. I personally ignore some of them because they're more likely just frustrated little children acting out, to be quite honest with you, or adults who clearly never grew up; I don't think I've ever been threatened by someone I thought really meant to carry out their threat; most of these idiots are just cowards that wouldn't have the man-bits to say jack-crap to our faces; they likely get off on scaring strangers because it makes up for how weak they feel in their "real" life. You know, how kids bully other kids at school, because they either get bullied themselves by kids at school, or by their parents, or siblings. I've been there myself... I was a bully for all of one day... at primary school... know what happened? I believe I cried and apologised to the kid; I recall us then being friends. Why can't bullies be like that? xD

Honestly, Facebook isn't that bad if you're just sensible with whom you add and always keep in mind that there could be an idiot at any turn, when commenting on outside stuff.

I've used Facebook for many years and not really had much in the way of trouble there. Sure, there's morons there, but you just ignore them, and if you really want, you can just ignore all comments and stick with talking to your friends, sharing stuff on your wall, and doing whatever else on there. I am, however, not one of those people with 300+ "friends"; I have 14 people there, 8 of whom are family or local friends/acquaintances, the rest are people I've known online for a long time and therefore feel I can trust them enough to have them on my Facebook wall and what-not. I choose very carefully with what I make public.