Not only can remedying a customer service error put things right, but you can win a customer for life.
Some important points:
1. Apologise sincerely, even if the customer is partly at fault.
2. Say how glad you are that the problem has been brought to your attention.
3. Empathise with the customer and the impact of the problem.
4. Fix the problem.
5. Make sure the customer is happy with the result.
There have been some high profile public remedies, like the recent Qantas offer of free flights as an apology for shutting down their global service in an industrial dispute.
It is said that a poor customer experience will generate its own impetus amongst social groups. Over compensation can result in a similar magnification of good news. A small concession at the right time can be very beneficial.