To duplicate: Make sure Advanced permissions is on.
Go to the Sitemap in Dashboard.
Click on a page to and change it's permissions.
Click Add Users/Groups
(Note, this only works if there are enough groups to cause pagination)
Click the next or the 2 to go to the second page.
Click any group to add.
Result: the window disappears but no group is added. The feature works if the group is on the first page or you only have 1 page worth of groups. This includes if you do a search and the result shows up on the first page, so the work around is to search for your group rather than browse.