This actually isn't that new. Google has been able to index a lot of stuff for a while, but it's now been made clear that over 53 million pages on Facebook have been indexed for search, and that means a pretty vast array of content. Since a page, a note, a discussion within a page or group, a group wall, a photo caption or video caption or title are all index-able, there's a lot more real estate to deal with.
One of the simplest solutions to protect the brand is reporting unauthorized use of trademarks, using Facebooks intellectual property form, however this can lead to a nasty group simply changing their profile image and adding fuel to the fire. I'm actually planning a different approach (pending legal approval). I'm going to reach out to the group owners. At the end of the day, if there is a product or service issue, any brand out there wants to know about it as soon as possible, and ultimately (if it's fixable) fix it. If there's an employee issue that's brewing, we have policies for that, but people should know that what they're saying could harm their career, not just with their current boss or company, but what about when they get googled in 5 years for their dream job and someone reads all the trash they wrote about their summer job 5 years ago?--not a heart-warming impression they'll make. --but most people either don't think that far ahead when they're trashing a brand online, or they don't care, or they simply didn't know that Google was listening. (...and Google is always listening...)
I think Facebook groups are great for friends and certain somewhat temporary situations, but I much prefer Pages and recommend them for brands or even organizations and associations, because they allow a measure of administration to the discussion. I would love to see Facebook put an expiry date on a group: Example-- If nobody adds to the discussion or updates the group for 3 months, the group disappears. This would ensure that people are only associated with things that they are engaged with, and could also allow fads and trends to die quietly. Example-- "The Get Claire on Facebook" group from 2007 doesn't really need to exist after Claire finally joins, however it takes all the members AND the group owner to Leave the Group before the group goes away. Did you know: A group owner can't just delete a group. If there are people in the group and the group owner leaves, the group still exists.
Anyway, the point of this post was to discuss the fact that Google knows all and is now, more than ever, reading everything that isn't behind the privacy wall on Facebook. Be warned! Brand owners: Try googling your brand like this and see what comes up [ brandname site:facebook ]
I bet you won't like all of it...