Jon, what a great post.  So many good ideas, as you mentioned.

Firstly, I'm reminded of when a bone is broken, and the place it heals ends up stronger than it was before.  Work processes or trust between individuals can be stronger than before because of the "mistake."

Secondly, I personally like to *capitalize* on mistakes in this way (meaning my mistakes or those of the managers I coach).  When my clients are worried because  they've made a mistake with an employee, I coach them that their humility and how they choose to handle *their* mistake with an employee can actually improve the working relationship and trust, i.e. their own leadership.  Seems a counter-intuitive way to view mistakes, but it's all in how you choose to look at it.