I had the same problem. The list of galleries/albums/list are loaded via an ajax call, so I had a look and found out the ajax call is getting a 403 Forbidden response. ( you can see the ajax call and response with Firebug).
The problem with my site is, that I don't have the WP installed in the root directory but in a subdirectory like this:
wordpress address (URL): "http://www.mysite.com/wp-mysite"
site address (URL) : "http://www.mysite.com"
And the ajax call is getting a domain via a WP function site_url(), which returns in my case "http://www.mysite.com/wp-mysite" and that's causing the problem.
I had to change it manually in wp-content>plugins>nextgen-gallery>admin>tinymce>window.php
In this file there is initialization of the autocomplete like this:
type: 'gallery',domain: "<?php echo site_url(); ?>/"
so I changed the php block "<?php echo site_url(); ?>/" for the correct domain:
type: 'gallery',domain: "http://www.mysite.com"
Please note I had to do it for all three types: gallery, album and picture and this is only a quick fix for me, as I don't have the time to look for a better solution. Once you reinstall or upgrade the plugin you'd have to do it again.