I"ll take the philosophical end of this question. Of course, that means asking another question; are there really any mistakes? Todd Smith has answered the Yes part of this beautifully, so I'll take the No side.
First off, my impetus is to start with a quote from one of my favorite contemporary French philosophers: “People know what they do; frequently they know why they do what they do; but what they don't know is what what they do does.” - Michel Foucault
As you can deduce from Foucault’s point about our awareness, it’s hard to imagine a situation where we can know if what we’ve done is truly a mistake. We may not like the outcome of a particular behavior we’ve exhibited, how others have reacted, how we’ve felt later after the incident was over, but can we really know if what we did was wrong on a Big Picture level?
There’s the Buddhist parable about the zen master who lives in the village and is revered by his fellow villagers. Every day they pronounce his very presence among them as a gift to their community until one day a teenage girl accuses him of impregnating her. As you can imagine the villagers are incensed and let the old Zen Master have it. Then a few days later the girl, sobbing, confesses that it was really a teenage boy on the other side of the village who is the baby’s father.
If the Zen Master looked to the external for validation about whether his actions, and really his very being, was in proper, a.k.a. unmistaken, alignment with the Universe, he would quickly become unbalanced experiencing self-doubt, low self-worth and have a difficult time being a confident contributor to the other villagers' lives. He looks within, however, and stays in alignment and self-congruent thus his ability to radiate love, kindness, and a plethora of positive aspects of character that he is known for by his community.
Mistakes lead us outside ourselves as we try to change, correct, validate, or even invalidate ourselves and others in order to be right as we have set it in our culturally conditioned minds. Undoing a mistake, then, is really about analyzing our capability to perceive from an elevated perspective so that we can engineer a more workable, livable approach to life. Otherwise, in our deep desire to be right, do good, and lead respectable lives we fail to understand that ultimately, life is unknowable. We waste time churning our inner lives into butter when really we wish to maintain a fluid, free flowing state of alertness, acting instead of reacting. Coming to terms with this essential aspect of living is the deep, palpable work of the human being being human which means being beautifully imperfect in our perfect relationship to the world.