Does that alone make social media, and agency branding, worth the investment—the amount of time and effort that needs to go into it? Back to the idea that a social media plan doesn't apart from a communication plan. Having an active Twitter feed, some cool YouTube videos, and a Facebook tipster program won't help officers' morale by themselves; if the agency invests in these but not in other forms of interaction, everyone will be thinking, “That's nice, but...”
Remember: social media is an amplifier above all else. It can either highlight the great things your agency is capable of, or (however inadvertently) display your weaknesses.
Which feeds into a third response to the questions: “Create a brand and you need to protect it.” The agency that invests in social media without integrating it into a full communications plan (or that pays no attention to how citizens talk about it, on and offline) is actually weakening its own brand. It may also indicate much deeper problems, such as the administration's inability to identify and devote resources to the true problem areas rather than the “flavor of the month.”
One agency focusing on the wrong things affects its own brand, but many agencies without a clear focus—acting independently and unaware of each other—can in fact affect the “police brand.” Is it time to revisit your interactions, online and off?