You can choose to have contacts in the groups sorted either alphabetically or by usage, with the most frequently contacted contacts at the top.
When viewing a group, the app also provides a means for you to manage the group, adding contacts to it or removing them from it.
If in the groups list, you see multiple groups with the same name, turn on 'Show group accounts' in the settings. In all likelihood, the duplicate groups come from multiple Gmail accounts, or having the same named groups locally on your phone and also in your Gmail.
The application has been updated so all functionality is there; it no longer requires the key for advanced options.
Full change log can be found here: http://goo.gl/HoZSBB .