"Do you remember the last time you sent an email and got a response back, within a minute saying, “FIXED. Really sorry that you had to experience that…” ?"

This is a perfect example of how you can turn a negative into a positive. From my own experience in the past I always noticed that if you make a mistake with a customer job but correct the mistake really quickly you actually form a bond with the customer that is much stronger than if you never made the mistake in the first place. You actually gain because of the error as long as the customer isn't in really bad shape as a result of it. (Of course you would get diminishing returns if you had to correct more than a small number of mistakes in any given time period obviously.)