Many organizations make "after action reports" and "lessons learned sessions" part of their standard routine.
While not all of those organizations are successful, I suspect that most successful organizations use such practices and their value lies not simply in avoiding the repetition of mistakes.
The other important benefits are:
Awareness. The word is out that all of the team members are supposed to be on the alert for ways in which matters can be better handled. You don't merely focus on achieving the results; you also are sensitive to the process.
Boldness. People and processes should not be fragile. Mistakes will happen and a goal is to make sure that all of the mistakes are minor. There are certain balls that the juggler must keep in the air.
Responsibility. Improving the game is not the sole responsibility of the team leader. All members have a role in assuring success and all should be open to ways in which their own specific areas of responsibility can be improved.
Although such analyses usually follow special projects and zero in on specific project-oriented recommendations, it also makes enormous sense to elicit weekly or monthly comments from staff members on their latest accomplishments and areas of frustration as well as the current state of their morale.
Those too will have a sizable impact on the success of future projects.