I've had this happen a few times and have approached in several ways. Would like the wisdom of the community on this one.
I've had directs (different people, similar issue) who have made a mistake and, proactively, stated "I dropped the ball on that one, won't let it happen again...".
Question for the community: do you say anything at that point other than "thank you, I appreciate your recognizing the issue and taking care of it for the future...?"
If the same behavior recurs I would address with feedback and it would reference the act that they essentially gave them self feedback (getting into systemic feedback, to a small degree).
Look forward to the opinions of the masses, thank you.