People posting nasty things on your facebook page...I've had them, I'm sure that you've had them, and although they make for good reading for other people, they're irritating at best and destructive at worst.
I did a question of the day recently about what people do when they notice a "facebook fight." The majority said that they find it embarrassing, but heck yeah, they're going to watch it unfold. If you allow this kind of thing to go on your public page, you're the one who's going to look stupid.
Now I know that people say that you should leave posts up to show "interaction" on your page, but there's a limit. I had one person who posted argumentative stuff so often that one of my friends who doesn't do cakes actually called me to ask "who is that woman on your facebook page?" I had been trying to be nice to this person, but after that I just went and banned her the next time she posted something. Yeah, it made her look bad, not me, but I don't need the aggravation.
I've also deleted things that were sexist, racist, religious-nutty and political. And some that were just nasty in general. There's no reason to leave anything like that up. If you enjoy debating politics do it on your personal page, keep it off of your business page.
I have my settings set so that people can comment on posts, but if they post on my page directly I get to see the post and approve it or not. This helps to stop people who just want to spam you, or people who are just there to talk smack. It won't stop people from posting nasty remarks in the comments on other posts, but if they do that you can delete the comment and ban that user.
I personally wouldn't bother reporting it to facebook unless it rose to the level of harassment, and if that happened I'd get the police involved, not facebook. The people who work at facebook have too much to wade through, and by reporting people who are just being obnoxious you're taking time from the really serious stalkers and people who are reporting things that really need serious attention.
The simple way to deal with the facebook nasties is to delete them. Just do it.
Kara Buntin owns A Cake To Remember LLC, online cake supplies at www.acaketoremember.com and www.acaketoremember.etsy.com