We all make mistakes, and when you are dealing with customers they are an opportunity to make a good impression. If you show you are willing to take responsibility and solve problems your customers are more likely to trust you.
I was at a restaurant last night and the kitchen made a mistake on my order. The waitress apologized and got a new order out in minutes. She didn't make excuses or explain away the problem. She took responsibility and acted right away. I will definitely eat there again because of the way the waitress took care of the situation.
How do respond when you make a mistake?