I think there are two kinds of mistakes. Both need attention. Both are learning opportunities. The only difference is that you want more of one and less of the other.
I want more mistakes from pushing the envelope, taking a risk and trying to make things better. These are positive, good mistakes, that have to happen all of the time or you are just standing still, not learning, and not progressing. I call these Heroic Mistakes.
I want less mistakes of the sloppy and disorganized kind. The type of errors that come from bad structures and bad management. I call these for what they are, Stupid Mistakes.
If you aren't pushing, aren't making Heroic Mistakes, your competition likely is, and the downside of these mistakes will be nothing compared to the downside of losing your business to the competition. I think in the heat of a moment we often forget that their are two types of mistakes; Heroic and Stupid, and we react with the same frustration and negativity towards a Heroic Mistake as we do a Stupid Mistake. Which just creates a culture of keep your head down and play safe. Which is ironic, cause this is the least safe place to be. Despite how frustrating the situation might be, I would celebrate and reward these situations. These mistakes are courageous and must be encouraged, shared, and if anything, serve as the inspiration for even more mistakes.
On the other hand, dumb, sloppy mistakes, call for an intervention. Too often these situations are not addressed, or worse, addressed in non-constructive ways that change nothing and the Stupid Mistakes just keep on happening. The best way I know how to do address these, with the least emotional freakout, is with Robert Fritz's Managerial Moment of Truth. I have never been a fan of the name but the process works! Get agreement on the situation. Then and only then, figure out what is, or has, caused it. For each "cause" identity the corrective action. And for each correction specify how it will be followed up on. It takes the emotion right out of a messy problem and let's everyone get right to the facts, and the fix, in no time. And of course, if mistakes keep happening and nothing comes out of the followup, you have the wrong structure supporting your people, or the wrong people altogether.
How do you reward a mistake? First figure out if it is Heroic or Stupid. And in either case, address it.