I'd love to put our logo on our Facebook group page (assuming that's permitted by SE policy). Is there somewhere a higher res version of our logo can be found?
I suppose could always take a photo of the T-shirt I was sent... :)
After asking @jmac, one of the CMs and having a chat with some of the other mods, basically it comes down to the rules in the Trademark page:
The logos associated with Stack Exchange Inc. and any Stack Exchange site are a trademark. The purpose of trademark law is to prevent consumers from being misled as to the origin of a product. So if you were making a product, and you used a Stack Exchange name or logo in your product (or in its advertising) in such a way that would mislead someone into thinking that your product was owned by, operated by, endorsed by, or in any way part of Stack Exchange Inc., you would be violating the trademark and this would not be legal.
Our logo images and site names are copyrighted. Any content on the Stack Exchange Network not contributed by users is copyrighted. Copyright is different than trademark. Ordinarily you couldn't copy it. But if you were writing a news story or blog post about a Stack Exchange site, reproducing the logo image would almost certainly be considered "fair use" and allowed under trademark law because you were not using it "in trade."
Other unofficial communities, such as arqade have used alternative logos for their purposes.
Perhaps an artisitic member could produce something :)