I am at a real loss at this problem. I just created a plug-in, and to log the actions in the plug-in (as I can\'t see the output of the processing), I added a hook to init l
After Rob Williams' answer I've read this post:
http://www.tastyplacement.com/how-to-remove-link-relprev-and-link-relnext-from-wordpress-head
And realized that the link tags with rel="next" and rel="prev" was running my init hook for a second time on my WordPress 3.5.1 website. These tags can be removed adding this to the theme functions.php file:
remove_filter('wp_head','adjacent_posts_rel_link_wp_head',10);
Do you have any links in the site (images, scripts, stylesheets, etc) that are 404'ing? If so, the default 404 page will display a "You are looking for something that is not here" page in the default site theme, so you'll end up getting the init hook called once for the initial page request, plus once for each bad link.
Doublecheck with Firebug and see if anything is being called incorrectly.