It happens even to the best of us from time to time - something thoughtless, inappropriate, or downright dumb gets said on a social network, people react, and next thing you know you've got a big scandal on your hands. In the context of a small or medium-sized business, even a minor uproar on a social network can spell big problems for you in terms of unhappy customers and a dip in sales. Just like in every other aspect of business, mistakes will be made from time to time on social media. Even if you're extremely diligent with your social media policy, there's not really anything you can do about the fact that people are human, and sometimes they say damaging or offensive things.
What you can do, however, is make sure you have a plan in place to deal with issues as and when they come up, so that you can handle any mistakes quickly and efficiently, with the minimum amount of damage. As is often said, the best cure is prevention, so having a clear and concise social media policy in the workplace is essential. The more people you have working with you, the more comprehensive and specific the policy has to be, as you are dealing with a variety of personalities, all of whom may have different interpretations of what "inappropriate" or "offensive" means.
Even if you're a sole proprietor, though, sometimes you might be your own worst enemy. I can't count the number of times I've seen people posting on Twitter or Facebook who were clearly drunk, angry, upset, or a combination of the three. It's one thing if you want to do that on your personal accounts, though I still wouldn't recommend it. On your business accounts, it's absolutely unacceptable.
If you do wake up one morning and find that you (or an employee) did the unthinkable and said something inappropriate on a social network, don't just sit there and hope no one noticed. Delete the offending post immediately, and issue a public and very sincere apology. Trying to talk your way out of it or accusing your audience of not being able to take a joke is not a smart move. The sooner you can apologize and make amends, the better. Most of all, use the experience to learn how not to play the social media field, and do your best to be a model social network citizen in the future.