A successful customer service survey has to get a lot of things right. You have to ask customers the right questions, and make sure they understand what you're asking. You have to continually monitor the process to make sure employees aren't manipulating the survey. You have to perform ongoing quality assurance to ensure customers' answers are being properly captured. You have to make sure you're contacting the right customers at the right time, and they are being surveyed about the right experience.
That's just on the data collection end. Then you need to deliver the right data to the right employees--easily thousands of reports generated daily--and make sure they have enough context to understand it. You need to make sure everyone has the right incentives to improve. You need to keep the entire process aligned with the company's business goals, and adjust as needed when strategic imperatives shift.
The biggest challenge in this whole process, however, is simply getting customers to take a survey.
Consumers today are often surveyed to death, and many customers don't feel that their input is truly appreciated. Automated robo-surveys are easy to ignore and feel very impersonal (if they work at all--I've found many customer surveys which are literally broken). While most customers are willing to offer their opinions, they are not interested in taking the time if the company will just ignore the survey.
That's why we often recommend immediate live interviews to our clients. While this is not the cheapest way to survey customers, it is by far the most cost-effective. Immediate live interviews have a very high response rate because they are very personal, and because you are reaching the customer at a moment when she is most likely to be willing to response. You can also go into great depth with 20-30 questions about what happened during the customer's experience, and follow-ups to ask about any problems or complaints.
A customer survey program is guaranteed to fail if not enough customers take the survey. In our world of jaded, overstimulated consumers, this really is the biggest challenge.