People who make mistakes and take them to heart spend enough time beating themselves up over it. It rarely makes sense to me to beat them up further. Punishment, scolding or worse can only make you look like a heartless and inconsiderate fool. If the mistaker openly acknowledges his or her mistake and you understand how the mistake was made, forgive the person and work together to find a solution.
People who make mistakes without notice or care do not deserve the same level of forgiveness. Far more fair to forgive a blooper than sheer ignorance and neglect. When running an organization, tolerance for miscalculations herein can only go so far. Make little room for bad attitudes, denial or blame. If a member of your team cannot accept mistakes as valuable learning or growing experiences, you do not want him or her on the team.