Emotional meltdowns are not OK.
Not all of us have rock-solid feelings, especially when we are passionate about the job we do. I know from personal experience how hard it is to not bite somebody’s head off when they are in my way. However, problems at work can lead to feelings of frustration or even anger when you come up against them. Don’t blow your lid off. Whether it’s a coworker or a subordinate who doesn’t see things your way, made a mistake, or actually failed to do something you trusted them to do, give yourself time to cool down. You still have to talk about it, but only after your brain has started thinking again.
From a practical side, most people will feel bad about a mistake if you tell them about it, no need to shout them down, too. Remember that you still have to work with them tomorrow. They have to trust you tomorrow. And if you’re a manager or a business owner, the odds that they’ll be buffing up their resume tomorrow goes up if you lose your temper today. Moderating your temper should be a part of your preparation for your management role, so use it.
Many companies in North America now have a “Progressive Discipline” policy, which forbids this behaviour. Depending on how it’s written, they may also forbid this with their “Workplace Violence” policy. I can’t speak for other places in the world, but it’s a common western thing, now. I think it’s step forward. Going off the deep end as you confront a colleague about a mistake can actually put YOU in the wrong. Watch out, lest your temper bring the HR wrath upon you. Companies whose policy includes an obligation to report unruly behaviour may earn you more than one simultaneous report for just one outburst!
Before taking that as my absolute position, I’m also thinking about the degree of the problem - it makes a lot more sense to be angry if someone’s negligence or deliberate action put another person in immediate danger. I know that I would be more than just assertive in a situation like that.
Another dimension is whether you are working with professionals or laborers. I think the difference is obvious, that the tolerance for losing one’s temper among professionals is much, much lower than it is when supervising laborers. Also, the amount of force needed in the control system is correspondingly different.
For everything else, maintain your professional decorum at all times.