Alex Raven

Report Post is a highly customizable plugin that lets your visitors to report posts or pages with inappropriate content. All these reports are displayed as a table in your Administrator section so you can decide what to do next: edit contents, unpublish posts/pages, or just delete these reports. The plugin was designed to work in both automatic and manual modes. In automatic mode, the link to report will be added to post’s meta box. In manual mode, you can place the link, button or image anywhere you want in templates.
Features:
<ul>
<li>Easy to use – you can simply activate the plugin and it will do the thing</li>
<li>Highly customizable via Options and CSS</li>
<li>AJAX based – no page reload will occur</li>
<li>Can be used in Automatic and Manual modes (to use in templates)</li>
<li>Works for Posts, Pages and Custom post types</li>
<li>Supports AJAXly loaded posts, ‘infinite scroll’ posts, etc.</li>
<li>Does not use additional databases / tables anymore. All reports are stored in postmeta.</li>
<li>Modal window instead of expandable form (works with AJAXly loaded posts!)</li>
<li>Bulk Unpublish, Publish, Delete Posts, Delete Reports</li>
<li>All texts displayed in front end are customizable via Options</li>
<li>Admin notification about reported posts</li>
<li>Can use Captcha to protect from spam</li>
</ul>
Plugin demo: www.esiteq.com/projects/wordpress-report-post-plugin/
<h3>Usage</h3>
Plugin handles 4 class names. Two pre-defined (.report-post-link for a simple link with exclamation mark icon and .report-post-button for button) 
and two custom that you can define yourself (.report-post-custom-link and .report-post-custom-button, respectively).
To work correctly, report link must be placed inside of an
<
article> tag. Article tag must have id=”post-XXXX”, where XXXX is the id of current post. If your theme does not use
<
article> tags, you can add post-id=”XXXX” attribute to report link, e.g.
<pre><code><a href="#" post-id="<?php echo $post->ID; ?>" class="report-post-link">Report Inappropriate Post</a>
</code></pre>

WP Report Post

Highly customizable plugin to let your site visitors to report posts with inappropriate contents to administrator / editor.

RaminMT

This plugin simply adds a button to Your site and let users report Your site broken links/problem and You can see them in WP dashboard. 
Description Box let You get site visitors name, email or anything You need plus description of what is the problem but if You don’t need this feature simply You can disable It from setting page 
With shortcode provided You can use plugin fully customized 🙂
<h3>Features</h3>
<ul>
<li>Fast & Light</li>
<li>Fully Customizable</li>
<li>Ajax Based</li>
<li>Secure</li>
<li>Dashboard Widget</li>
<li>Simple to use with shortcode, jQuery selector and default button</li>
<li>Description Box to get email/name of clients and their descriptions about problem</li>
</ul>

Links/Problem Reporter

It's a Sexy and Nice plugin to get reported your site's Problem/Broken Links

WP Report Post vs Links/Problem Reporter