It's going to happen.
No matter how tight a ship you run, there is going to be those times where you or one of your staff members are going to goof up and do something wrong to a customer or a customer's order. Shipping the wrong item, swapping labels, forgetting to include items--all these things are quite common regardless of the technology in place. When humans are involved--errors happen.
Now, don't think me crazy, but it has been my experience that this is a good thing to happen once in awhile. Totally serious. Yes, it costs money to fix the problem. Yes, it sucks having to deal with an angry customer. Yes, it can strain the "flow" of your order processing procedures. But, it can all be worth it.
When a customer calls (or emails, txts, whatever) with nostrils-a-steamin' in anger regarding a screwed up order, they don't care about your excuses or double-talk. All they want is for this to be fixed quickly and without an ounce more effort on their part. And rightfully so, considering they have trusted you with their personal information, their private financial information and your ability to give them what they want quickly and efficiently. There is a right way and a wrong way to handle this. Here are some examples of the wrong way to handle this (real life occurrences):
"Let's see if this was our mistake or yours."
"Oh, that was a mistake in a different department. Let me transfer you."
"Are you sure you got the wrong thing?"
"Well, we can send a replacement, but it will take 2-3 weeks."
"Fine. Ship the wrong product back to us and we'll send you the right one."
There is only one way to handle a situation where the fault is 100% with the business.
"We apologize for the error with your order, Sir (or Miss), and we will get the correct product out to you TODAY along with a postage paid label (or box) for the return of the incorrect item. We will also be sending you out a small gift with our apologies to thank you for being so patient with us. Sorry for any inconvenience this may have caused you."
That's it. Nothing more or less. Three sentences that will, in most cases, not only placate your customer, but in my experience, earn you a customer for life for showing that your business truly gives a hoot about fixing a mistake. Word of mouth is stronger than ANY advertising system in the online or offline market today, and with this, you just earned a piece of it when your customer tells a friend..."Y'know, XYZ company send me the wrong item, but with one call they were so efficient about making good on it that I will DEFINATELY deal with them again. No hassle at all."
Just remember though...while this can be good for business once in awhile, getting word out there that you consistently goof up orders will have the complete opposite effect, so keep those organizational procedures nice and tight. Oh, and if you goof up that same customer's order a second time (even years later) then you've lost them for life.