After upgrading a client's site, I noticed that the plugin's Manage Album page breaks in WordPress 3.5. Namely, you can't grab an album and drag it to a gallery.
Here's the fix to get this to work again.
Go to the plugin directory and open this file: \wp-content\plugins\nextgen-gallery\admin\admin.php
Go to line 257 (or near it) and find this line and comment it out:
"wp_enqueue_script( 'jquery-ui-sortable' );"
"//wp_enqueue_script( 'jquery-ui-sortable' );"
This will remove the plugin's reference to the jQuery 'sortable' class and fallback on WordPress' usage of it.
I can't confirm this works for every instance, just did for me.
As a reminder, if/when the plugin author updates the plugin, you may need to do this fix again. Hopefully they will roll this fix into the next iteration.