How to manage a situation where a junior does a mistake in daily operation works?

When a Junior does a mistake in a daily operation works, Immediate Superior of these junior employees should take the full responsibility since it is under him/her. Supervisor/Manager should analyze what when wrong that the Junior does a mistake, is he is she is properly oriented of this daily task? does he or she have provided a job description  as  guide to his daily task. If those qualifying questions have not met, the immediate supervisor or Manager should have a re-orientation of the operations, his/her task. Have a regular monitoring of his/her daily work until he already managed his/her task. Manager/Supervisor provide him/her a training to be able their staff to be fully knowledgeable and equipped to do his/her tasks. Coaching and mentoring can also provide to the junior staff to ensure that he/she deliver the required output.

mistakes are made due to lack of knowledge or concentration find out these problem and encourage them to do better 

I believe you asked the wrong question. Juniors mistakes always will be there and most of the time you have to cross check the task they are doing is right/wrong.

Actual problem is "How to manage a situation where a seniors does a mistake in daily operation works" . Specially your manager or who is directing you

I believe this is more difficult ;)

I have two direct reports with two very different working styles.

One is more independent and usually runs with the project — she asks me for help or advice if something comes up. When she shares various projects with me, there are usually a couple of minor items that need correcting, which I share with her for next time. The next time she shows me a project, I see the same items that need correcting. I started to wonder if it was my communication style, so I also shared the corrections via email so it’s in writing. But the same thing happens again, regardless if I talked to her about it or wrote it down.

My second direct report needs a little more hand holding so there is constant communication. There are two extremes to his working style — he either gets wrapped up in the details and forgets the project objective so I need to bring him back on track or he rushes to finish the project, but neglects the details so there are multiple revisions and drafts. As with my other employee, I have communicated the project details and objectives verbally and also through email so he can refer to his notes, but I find him making the same errors or not paying attention to the details when we work on the next project.

One of the things I have wanted to avoid since becoming a manager was to not micromanage my staff. I understand there needs to be some micromanaging to make sure the team is on track with company goals and to make sure their priorities are clearly understood so they don’t waste their day working on unnecessary items.

Without becoming an uber micromanager, how can I communicate to my two reports that they need to pay attention to the details because the same mistakes are constantly being made and it is noticed not only by me, but the clients if they don’t show me the drafts?

I do not know if they are not listening to me or they are working too fast and forget. When I share my thoughts and offer suggestions I try to explain the reasoning so they both know, it’s not because “I told you so!” but actually the reason why we “use this terminology” or why we “decided to go with this format,” etc. I’m at the point where I really want to say (but never will), “This has happened multiple times and it shows that you are not listening to me — you need to start showing me every project you are working on because I no longer can depend that you are learning from past mistakes and putting effort into your work.”

It sounds like you’re so focused on not wanting to be a micromanager that you’re missing the fact that your employees have legitimate performance issues that you should be addressing.

It is not micromanaging to clearly explain what a work product or outcome should look like, or to ask that work be done correctly, or to expect people to incorporate your feedback into their work in the future. That’s managing.

Based on my experience on working, if one does a mistake in an organization, you should help one another, because I believe in helping to lift co-workers up in an organization is not a problem nor it can decrease your reputation, It will be greatly appreciated if one can really help what to do after that mistakes,after-all we should learn from other mistakes or self-mistakes too.