I made a mistake with a query at work (nothing major at all) and a colleague picked up on it.
She then decided to go straight to my manager and write a long email about what I'd done and that she'd now put it right.
She never said a single word to me herself, or at least cc me into the email.
I come across mistakes all the time and if its just that (a genuine mistake and not a training issue) then I just correct it and move on.