I'm sorry to complain since I know you've spent a lot of time and effort working on this.
The problem with this plugin, like so many other plugins, is that it messes up the html and thus breaks validation. HTML output after plugin-activation:
<p>...Paragraph text...<br /> <a name="rubrik"></a><br /> <h3>Rubrik</h3> <p>...Paragraph text...<br /> <a name="rubrik-2"></a><br /> <h3>Rubrik 2</h3> <p>...Paragraph text...</p>
Two open paragraphs and a bunch of nasty
<br /> tags that adds unwanted whitespace.
Hope you can look into this and fix so that the html validates. It'd also be good if you had a class for the anchor so that you can target the link with css:
<a class="mwm-anchor" name="rubrik"></a>