EDIT: Just to update this "answer" I wrote a tutorial on SSbits (http://ssbits.com/adding-fields-to-page-comments/) - Hope it helps

@MarijnKampf

Let me explain what I have done, in my examples I am adding an email field. Also note that while this does manage to add the field the the CMS CTF (Complex Table Field) it fails to add it to the popup.

Here goes:
File added - CommentAdminDecorator.php (in mysite directory)

<?php

/*Copied EditForm from CommentAdmin.php version 2.3.1
    - Added Email field
 */
class CommentAdminDecorator extends LeftAndMainDecorator  {
    
    public function Link(){ //had to add errors out as missing function if not
        return $this->owner->Link();
    }
	
	public function MyEditForm() {//Was originally EditForm, wasn't showing in the template so I had to create my own template
......
		$tableFields = array(
			"Name" => _t('CommentAdmin.AUTHOR', 'Author'),
			"Comment" => _t('CommentAdmin.COMMENT', 'Comment'),
			"CommenterEmail" => _t('CommentAdmin.COMMENTEREMAIL', 'Email'),
			"PageTitle" => _t('CommentAdmin.PAGE', 'Page'),
			"CommenterURL" => _t('CommentAdmin.COMMENTERURL', 'URL'),
			"Created" => _t('CommentAdmin.DATEPOSTED', 'Date Posted')
		);	
		
		$popupFields = new FieldSet(
			new TextField('Name', _t('CommentAdmin.NAME', 'Name')),
			new TextField('CommenterEmail', _t('CommentAdmin.COMMENTEREMAIL', 'Email')),
			new TextField('CommenterURL', _t('CommentAdmin.COMMENTERURL', 'URL')),
			new TextareaField('Comment', _t('CommentAdmin.COMMENT', 'Comment'))
		);
......
	}
}
?>

<div id="form_actions_right" class="ajaxActions">
</div>

<% if MyEditForm %>
	$MyEditForm
<% else %>
	<form id="Form_EditForm" action="admin/comments?executeForm=EditForm" method="post" enctype="multipart/form-data">
		<p><% _t('WELCOME1', 'Welcome to the') %> $ApplicationName <% _t('WELCOME2', 'comment management. Please select a folder in the tree on the left.') %></p>
	</form>
<% end_if %>

<p id="statusMessage" style="visibility:hidden"></p>

I hope this helps! If anyone comes up with why my popup isn't picking up the field please let me know!

-Dan