This is very similar to a question posted last September, but I haven’t come across any working solutions for it (and am not versed well-enough in session cookies to do it myself). If I’m having the user authenticate in WordPress, how do I read that session cookie with MediaWiki such that the user then has permission to edit the wiki? I’d like to have WordPress handle all of the user data, so the login would always happen within WordPress.
Sharing WordPress session cookie with MediaWiki
A little bit of a late answer, and this might not be the perfect solution you’re looking for, but I’ve been using AuthWordpress.php for the past 9 months or so without any issues. While WP login sessions aren’t persisted when going to the Wiki, WP users are all authenticated properly when logging in from the MediaWiki end. So you just login to the wiki with your WP credentials.
Looks like the best way to get this is here: http://wordpress-malagasy.googlecode.com/svn/wp/misc/wordpress-mediawiki/AuthWordpress.php. And just follow the directions in the comment at the top.
Hope that helps!