Did some further testing around this evening (thanks, DrBob and KaoticEvil, for playing along), and have some more thoughts...

- No matter what the security level of the group is, any one who is logged into the forum can see any posts in the group area. The only difference is that people who aren't members of the group can't post.
- For anyone who starts a group, you moderate the group. If you set a higher level of security, you get to invite members and/or accept them. It's not a lot of work, but would get awfully annoying if it were "invite only."
- Personally, I see little reason to set any permission level higher than "open registration." Since everyone can see the posts, you don't have protected info. Set it as open to keep the workload down.
- If you start a group, you do NOT have the ability to delete the group. Maybe this is something our admins can change? Alternatively, leave it as-is and just bug the admins if/when you want to delete a group.
- You can boot members if you need to. Just an FYI...
- More and more, I'm thinking the groups area is best when trying to keep things out of the forums, so as not to overpost there, and allow people to select themselves in to specialized discussions.

I'd encourage others to try out the groups area and try to play with features I haven't used. Again, just posting my thoughts...