Scenerio: Someone is upset over something. They either had a bad day, they have a chip on their shoulder, the moon isn't aligned or they just wake up on the wrong side of the bed. They come into your store, they don't like something, they wait too long, they didn't like your selection, they felt you don't carry enough blue, you were on the phone too long, you made them wait 10 minutes too long for their appointment or something along those lines. The next thing you know, they have gone onto your Facebook, blog, or twitter and spread a whole lot of one sided information about what happened also on their own wall and on any other wall they can get their hands on. It is malicious and it is against the law.
Monitoring of your Facebook page especially, if you are a company is important and needs to be done daily. Negativity can work against you or it can work in your favor. If someone is talking about a particular product or service you can address your willingness to make things right with the person publicly or privately. If you do it publicly, it will show others that you are eager to make things right which shows good business sense. If the person comes back again, you can take the conversation private and deal with them to right the situation coming to a mutually satisfying agreement.
However, if the person is continually, aggressively hurling insults and false accusations on your wall, you can and do have the right to remove any message from your wall. If they continue to bad mouth or bash you, you can ban them from your wall.
Business and personal are two very different things. If you feel someone is maliciously attempting to make you lose business this is illegal! You can and should file a police report.
Do not fight back publicly, this is is not only unprofessional but will appear petty in the public eye. You can issue an apology to your clients/readers addressing any negativity anyone has had to endure on your wall and let it go.
Your next step is to highlight positive information and messages backing up what you already hope everyone remembers about your business. Showcase your goods, your service, comment on your customers comments, etc., anything that will bury the negative impact your business may have suffered.
This is one of the reasons companies hire Social Media Specialists. Regular blogging, commenting, and monitoring of your Facebook wall is a necessity and maintaining a positive stance in your business will only bring you success. You cannot control what someone will post on your wall but you have the power to make sure there is a great deal more positive information than negative information for all to see.