I have written extensively about how dot-govs are passively listening to all that happens on social media. They mine way more data being passive than they would by any active engagement as Jason suggests. I am currently writing about many of the social media's transparency reports, including Twitters. 

http://blog.twitter.com/2012/07/twitter-transparency-report.html

The phases of cyberwar: first comes the passive-aggression. Statements that seem to be not directed at anyone in particular, but in fact, they really are. Second, the insults and direct verbal war. And third, as Mitch has said, the hacking begins.

I'm sure the US will someday use Twitter, Tumblr or whatever the latest social media platforms are to influence and inform.  What fascinates me is the pooling of information, okay - propaganda, that collectively results from several sources pushing out content via social media.  The varying views en masse have the potential to tell the holistic truth with the result leading to more global transparency than we've ever experienced before.

@Jason The cyberwar. I've seen so many takes on this, and some, like Social Warfare: Israel Live-Tweets Its Military Campaign Against Hamas, really fail to see the forest (real war) for the trees (or, in this case tweets and status updates). Today Tablet ran a piece called "The 'Kids' Behind IDF's Media"

The goal, as Dratwa explained it, is twofold: to get Israel's narrative out in real time, as people read about red alerts in Tel Aviv and rocket landings in Gaza on Twitter, and to cut out the middleman of "old media" in communicating with pro-Israel activists. "What we try to do is to be fast and get information out before the old media," Dratwa told me. "We believe people are getting information from social media platforms and we don't want them to get it from other sources—we are the ones on the scene, and the old media are not on the scene as are the IDF."

It's not immediately clear what concrete impact the IDF's Twitter battles are having on the course of public opinion. Foreign journalists have been allowed to enter Gaza during Operation Pillar of Defense—a change from Israeli policy during Operation Cast Lead, when foreign journalists were barred from Gaza—resulting in a steady stream of gripping footage and images from the territory. But the IDF boasts 185,150 Twitter followers viewing its stream of videos, photos, and updates, which includes information from the front and frequent reminders of Israel's ongoing provision of food and medical services to Gazan civilians.

From my own perspective, I think there is a serious downside to that approach as a number of articles like http://readwrite.com/2012/11/15/unbelievable-the-idf-has-gamified-its-war-blog, put a spin on the whole thing and the encouragement to share as treating war like a game.

As for questions of censorship, Mathew Ingram brought up that question in http://gigaom.com/2012/11/15/israel-and-twitter-where-does-free-speech-end-and-violence-begin/: 

 And while they have all expressed their commitment to free speech in some form or another, they have absolutely no obligation to uphold that, or to tell users when information has been removed, or why.

We may have disrupted our old information gatekeepers — newspapers, television, even governments — but in many ways we have just exchanged them for shiny new ones. And they are just as inscrutable, if not more so.

I expect we'll see denial-of-service and other attacks directed at both the Israeli and Palestinian accounts.

Wars have always involved propaganda fights; this is the latest iteration.

One of the big dangers of social media in combat is that soldiers might accidentally reveal confidential information that can help the enemy.

@Kicheko

Good point, if the U.S. government does one day engage in image engineering via say live-blogging military actions on Twitter/Tumblr, then it could be accused of pressuring such services (as they're domestic) to skew the coverage.

Of course I would be high wary of such claims given that I think the companies involved would complain -- just look at how vigorously Google resists DMCA takedown notices and other forms of potential censorship.

I do think, in a sense, such image engineering is somewhat inevitable for the U.S. military as it becomes more ubiquitous...