Mistakes happens. I've made them, you've made them, we've all made them. As a manager, you're not only responsible for your own dumb mistakes, you're responsible for every one of the mistakes that each of your employee's make.
Given all of these mistakes, there's a lot of potential opportunities to practice how you respond.
You have two choices:
You can lose your temper, yell, scream, embarrass and punish the employee. While that approach may produce a temporary feeling of euphoria via an adrenaline rush for YOU, it'll only makes sure your employee will do everything they can do to ensure you never find out about future mistakes they make. In other words, they'll get really good at covering up, and not so good at accountability.
The employee will most likely also think you're an $&*#-hole, and no one wants to work for an $&*#-hole. Oh, and the next time you make a mistake - that's the one the employee won't be so careful to cover up.
A better approach is to step back, take a deep breadth, and look at each time an employee makes a mistake as an opportunity to lead and develop the employee.
Here are tips for how to respond to an employee's mistake in a way that develops, vs. punishes, and provides you an opportunity to shine as a leader and earn your employee's respect and loyalty:
1. If the employee discovers their own mistake and comes to you, thank them for being accountable and bringing it to your attention. Let them know that mistakes happen, and it's important to you to acknowledge them and fix them as soon as possible.
2. Be a role model for the above behavior by publicly acknowledging your own mistakes.
3. Don't focus on placing blame - focus on solving the problem and making sure it doesn't happen again.
4. Ask questions and listen - without judgement - in order to gather all of the facts.
5. If appropriate, ask the employee what they think needs to be done to solve the problem and make sure it doesn't happen again. In most cases, people will know. If you rush in to solve the problem yourself (and sometimes you may have to), you miss the opportunity to coach and teach the employee to think for themselves.
There will be times when an employee just won't know what they did wrong and how to solve the problem. That's the time to practice situational leadership, and switch from coaching to teaching. You might have to spend time explaining to the employee WHY what they did was a mistake, i.e., it was a violation of a policy, the negative impact it has on the business or customer, etc...
Almost every mistake can be treated as a development opportunity. You may as well - it's a sunk cost, and not harvesting a return on the investment is bad management.
6. Separate the behavior from the end result. Sometimes, the employee practiced all the right behaviors, but didn't get the desired result. Other times, they'll get the desired result, but do it in a way that you'd never want them to repeat. By asking questions and listening (tip #4), you'll be able to learn what to reinforce and what to correct.
7. After the meeting, take some time to step back and examine the system, process, structure, etc... that may have contributed to the mistake. Maybe similar istakes can be prevented with better training, communication, and/or procedures. Mistakes rarely have just a single cause, and people are not always the problem.
A measure of a leader is the impact you have on every employee's energy level, or morale, after an interaction with you. Chances are, if they came to you with a mistake, they were dreading the meeting and already feeling pretty crummy about it.
This is often the time when an employee needs to know it's OK - that it's not the end of the world, and you're not going to hold it against them. I'm not saying the mistake should be minimized, especially if it's a doozy. However, once an action plan is agreed to and lessons were learned, make sure the employee leaves the discussion with their head held high and feeling confident in their abilities. They will always remember that moment - not just because they learned a valuable lesson, but they'll remember what you did for them as a leader.