Node Gallery makes use of jquery and optionally of the jquery_ui module. Some drupal modules, however, require a newer version of jQuery to work. If for example you choose to use colorbox to display your images, you also need to enable the jquery_update module. This might cause some problems, e.g. the custom sorting of gallery images might fail. This is due to a conflict between your version of jquery_ui and the jquery version provided by jquery_update.
You can see what versions are in use of your site if you visit your status report page. The version of jQuery targeted by a release jQuery UI are mentioned in the release notes. As a rule of thumb these combinations work well together:
So check which version of jquery is in use and (if necessary) install a compatible version of jquery UI. If you don't know how to do that take a look at this tutorial: http://drupal.org/node/1078080
After uploading the new version of jquery_ui you only have to flush your caches (at mysite.com/admin/settings/performance or via the link provided by the admin menu module which you should be using) and you are good to go.