What should leaders do with anonamous letters and comments that come to them in their leadership role?
Ignore them! In not being willing to identify themselves they have taken the cowardly way out.
What should leaders do when people see that they are leaving their organization either as staff or as constituents?
Listen to them! Ask why they are leaving. It is better to know than to not know. You may not change anything but you may learn something.
If you are in a change process and people decide to bail, what should you do?
Nothing. Be gracious but don't change your plans because people complain or leave. When something changes, people will complain. Be gracious but don't appease.
If you have a vocal critic in your congregation. Before you engage with them check their giving records.
Those who don't give regularly in the church don't have standing to complain because they have no commitment to the church. I will listen but will not receive their criticisms as valid.
If people complain with poor attitudes toward leaders or your organization...
Remember that those who don't live out the Fruit of the Spirit will not help you get to to where you need to go. When people violate the law of love in their attitudes they cannot help your organization smell like Jesus.
If people tell you that they are leaving your church...
They have already left in their heart. They have moved on in their minds so trying to convince them to stay is not helpful. They may come back on their own at some time but don't try to change their minds.
If someone puts private pressure on you to change something or do something...
Don't feel pressured and get counsel from others rather than allow the voice of one individual to create angst in you. If it is a trusted friend who you know has your best interests in mind, listen. If it is someone with a personal agenda, be wary.
If you are attacked by an individual whose words, actions or attitudes are unloving...
Their attitude which is anti-Jesus should compell you to take their words with a grain of salt.
Remember this. All leaders face criticisms and complaints. We live in a highly conflictual time where people are venting in all kinds of unhealthy ways. Who shares criticism with you and how they do it is a critical factor in how much you should listen. Everyone has a plan for your life but the only one whose plan matters in the end is God's.