From the perspective of learning about their agency, I can't help too much. However, from the sharing aspect I have a few suggestions. (a) Establish an agency-wide social media policy similar to IBM's, which is considered the gold standard. Basically, it removes the idea of "approved" content, and let's everyone use social media however they want, even if they put down the agency. This shows authenticity, which virtually no agency has in "approved" content. (Does anyone really believe all the good things coming from press releases?). (b) Encourage the use of social media tools such as blogs and Twitter. (c) Provide training on using these tools.
These 3 steps will go a long way toward making employees want to share the wonderful things their agency is doing, both the good and bad. (And believe me, sharing the bad isn't a bad thing).