Seth Godin raises an interesting point in his post.
Dealing with an angry person can be an opportunitity or a drain on your business. His point is quite valid though, unless you can deal with the anger, you cannot move foward with any other subject or rational action.
If the person is not angry with you or your company you may have a huge opportunity. If you can resolve the problem you may have won yourself a loyal customer. However, you need to potentially spend a lot of time getting to the root of the issue. During this time you need to decide if the anger is chronic (if so find another customer unless you are an anger management coach) or if brought on by a rare situation.
If the person is angry with you, your company or your product there is is still opportunity. But you need to really listen and be prepared to take action. You may have already lost this person as a customer, but if the concerns are valid, you need to fix the problem. If its just a bad customer you may be better off moving on. Either way its an opportunity requiring careful thought and a decision.