There is a tendency for some organizational leaders to fall into a mindset that they have to be right to justify people's continued faith in them. I think this misses the mark, and fails to give people enough credit. No one believes that leaders always get it right. People will follow a leader who is authentic, and that includes admitting to one's mistakes rather than doubling down on them.
I am a fan of the book The Four Agreements, by don Miguel Ruiz. Two of the book's tenets come to mind: Be Impeccable With Your Word, and Always Do Your Best (realizing that your best may vary from moment to moment). These simple concepts encompass traits of good leadership.
To foster a healthy organization, leaders should embrace being wrong. A leader who lives out this vulnerability demonstrates to the workplace that it is ok to make mistakes while doing one's best.