Themes: From a branding perspective it would be very useful if you could apply some formatting to an individual Facebook Group. There is an option to insert a logo/banner for your group but it simply doesn't cut it.
Feeds: I bet many companies and bloggers would love the ability to post an RSS feed of their latest posts or news stories inside their Facebook group rather than having to use "posted items." Additionally, your community should also be able to subscribe to your RSS Feed.
Ratings: Posted Items can be useful in helping spread the word about useful industry news items to your community, however it would be even more useful if your community could rate the usefulness of a given item so that you could provide them with more from the same topic.
Analytics: I have been asked this many times before, Is there Analytics for Facebook Groups? Ideally I would love to see a dashboard which showed users' time within your Facebook group, interactions with the wall, interactions with the posted items, new visitors, geographical break down of users and attrition rates.
Surveys: It would be very cool if you could host surveys inside your Facebook group, allowing you to poll targeted members on topics related to your industry, your company or your content.
Can't say anything other than that I totaly agree with you. Even the most basic functions like searching for members is missing. That really pisses me of when I have more than 10 000 members in one of my group and I really want to kick out this one guy.
And surveys, that would be really awesome.
You're right in that the basic search functionality and management of users is quite lacking in Facebook. It makes it difficult to leverage such a valuable community of users.