How to add a class to the webform error message
I think the short answer is no, since the errors set in the error message box could come from any source, meaning the errors in that &lt;div&gt; aren't necessarily just your webform errors. Since it looks like you're using your webform as a block I'm guessing you can't target a body class to check if you're on a particular page type either.

If you were setting your own error messages you could add a &lt;span&gt; around the message with your custom class, but that would mean bypassing the validation handling webforms provide.

One possible solution would be to use JavaScript to find &lt;li&gt; elements that have text matching the error messages you want to style and moving them to a custom container. Another could be creating a YOURTHEMENAME_status_messages() function in your theme's template.php and doing a regular expression or string comparison to output specific error messages in a separate container. This route would affect all error message using the same text though, so it could affect an error message that was not from your webform.