Complaints are great. Although there is a tendency to do the same with complaints as with a medieval runner bringing bad news from the battlefield – blame the messenger – this temptation must be avoided at all costs. Complaints are the best and most unvarnished source of customer feedback. That's when they are read in the raw, uncorrupted by staff editing, "summarisation" or by any other subtle bias from your customer surveys.
It's much better to hear from a customer, and have the chance to fix things, than for them to bad mouth you behind your back, or even worse, broadcast your failings for others to hear. A customer who has been able to complain, and feels that the complaint has been taken seriously has already reached the first base in changing their feelings about your organisation. They are then much less likely to spread their complaints more widely.
Customer complaints highlight problems with people or processes, often way before other indicators show red. You can then fix them before they cause too much trouble. It's all too easy to glide blithely along while significant problems are developing, with no recognition at management level. Complaints help to shatter the peace, for the better.
If you don't already have a customer feedback facility on your website, consider introducing one. Ideally hosted by a third party so people know that the comments are authentic. You'll get positive and negative input, and make sure you respond to the latter saying how you've tackled the issue.
Research has shown that customers with issues that are resolved quickly often become very loyal, which is good for all involved and often helps boost the bottom line. In other words, listening and fixing complaints creates better customers, and better customers are more profitable.