Deciding on the best moderation strategy is an important part for any business on Facebook, or on any social network for that matter. Deciding whether to delete a potentially negative comment needs more thought and consideration than you might think. "The first thing that comes to mind when a business fears feedback from social media, is that they are more important issues that need to be sorted before even venturing onto social media. Your business really should not have a problem with it. In fact, if you are managing customer expectations, and are reliable and accountable to your customers, you have nothing to fear."
When you are on social media, you must always think as though you are the customer. One of most important roles as a business is really to listen and solve problems that your customers may potentially be having. Therefore you should think about how your audience will react to anything that is said and done by your company. For example, deleting a post may send off signals to your customers that you are not listening to their problems and as a result you are ignoring problems in your business. In reality, such a customer is helping your business because they are identifying issues which when sorted will help your business prosper.
You should treat you fans, and followers as if they are your “real” friends/business clients. Your customers must ultimately feel as though they can trust your brand and your company, and by doing so you will remove any barriers people might have when interacting with your business.
Having an open relationship with people will not only give your business more of a likability factor, but also help you to understand your market at a much deeper level. It will allow you the be the fly on the wall as your customers interact with each other. A while ago it would have been unheard of to get this amount and depth of market insights, but now you can have your customer base right under your fingertips (literally). Moreover, having an open relationship will foster fans that are willing to stick up for your brand, which is not only great social proof but displays a kind of loyalty not really seen before in a public way towards companies.
If, however, your company has decided to delete comments, maybe because they are obscene, have a “House Rules” custom tab on your Facebook Page. It is a good idea to have guidelines for your page, including what you will not tolerate i.e. swearing, threats against any other member of the page etc. Then if there is a complaint, you can point them to your 'House Rules" which outlines clear guidelines for your community. A word of warning, do not try to control the situation too much. As a business, you are entering people's personal lives and space. If you are too harsh you will get very negative reactions, most likely ones like "we can do whatever we want, this is ... (e.g. Facebook). Be lenient, and fair.