A summary of a recent Demos (UK think tank) report:
the Twitter conversations between the Metropolitan Police and the public following the vicious murder of Drummer Lee Rigby in Woolwich.
Capacity is an issue when, astonishingly:
...45% of the 19,344 tweets they analysed were produced by a single bot network...
It concludes:
...this surge in social media interaction with police is obviously a mixed blessing; there is a small amount of potentially useful information included within a torrent of hearsay and rumour plus the inevitable general noise of people just participating in the #Twitcident without any particular motive.

It seems to me that there are two key social media challenges to police in the aftermath of major incidents:

To ensure that there is extra capacity to monitor social media accounts and ensure that accurate, timely and rumour busting information is sent out at regular intervals.

To have in place a sophisticated system to analyse tweets to provide intelligence and insight.
Link:http://us2.campaign-archive1.com/?u=...&id=b60a7d789b

To actual Demos report:http://www.demos.co.uk/publications/metpoliceuk