The Facebook page for MathOverflow is currently pulled from the Wikipedia article. The Twitter account has no avatar and only 90 follows. The most active is the Google+ account, which posted about moderator elections 5 months ago.
It would be nice to see MO have more of a social media presence.
Would you be interested in converting the FB page into an official page, and having it be managed by the MO community? Being a social-media manager (or content curator) for MathOverflow could be an elected position, like being a moderator on the site.
This could also tie into the thread on how to emphasize MathOverflow's best content: post it on social media, and target influencers to share it (e.g., Terry Tao).