I've made a full fresh install. My support env. is Xampp version 1.7.7, which is very close to the one of my hosting company (same PHP version 5.3.8, same mysql version 5.5.16).
I did install WP 3.8.1, BuddyPress 1.9.2, bbPress 2.5.3.
WP permalink settings: Numeric, as http://localhost/wordpress381/archives/123
Optional Components activated in BuddyPress: Extended Profiles, Account Settings, activity Streams, Notifications, User Groups. Settings left as by default.
bbPress: default settings plus groups forum enabling.
Creation of one user (user1) as an author,
Creation of one forum (forum1),
Creation of one group public (group1) by administrator, plus one member (user1). Attachment to forum1.
Creation of one topic (topic1) in the forum1,
Installation of Nextgen Gallery 2.0.58 (unfortunately, the version change today !). Do not activate.
Go to the homepage, click on the "groups" link => OK
Connect with admin account,
go to homepage,
click on "Groups" (http://localhost/wordpress381/groups). => http status code 301, Moved permanently, with http://localhost/wordpress381/groups into the location header.
And so, issue still there.