Mayank Kumar

This plugin will help you to display the number of comments in different categories and adds a widget to the WordPress dashboard.
<h3>Installation Process</h3>
From your WordPress dashboard
<ol>
<li>Visit Plugins > Add New</li>
<li>Search for “User Counter”</li>
<li>Install and Activate User Counter from your Plugins page</li>
<li>Bingo, your plugin has been activated, and your widget is now in your WordPress Dashboard.</li>
</ol>

Comments Counter

Display the count of all types of comments.

Gurmeet Singh

With this plugin you can restrict your users to view the unapproved comments in dashboard of multi-user site. Even you can restrict administrator and editor also. So, only the approved comments will be visible in the dashboard.

Approved Comments Only

Restrict user to view the unapproved comments in dashboard.

Comments Counter vs Approved Comments Only