@chadwicksjs: I don’t think this is a WP 3.6 problem. We’ve updated quite a few 3.6 sites and none have this. We’ve seen one other user report some thing similar but on a 3.5.2 install.
If you’d like us to look directly into this, you can send us WP and FTP login credentials via our bug report and we’ll look into it directly.
http://www.nextgen-gallery.com/report-bug/
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If you don’t want to do that, I’m wondering if you can tell us if you are on a window-based hosting platform, or if you are using different WordPress vs Site URLs under General Settings?