This includes traditional and social media.
A danger point for all senior personnel dealing with a disaster is in communicating with the media, in all its forms. Today that includes social media, and no, the answer is not to avoid the danger.
Crisis 101 blog post that just precedes this one has some good advice on dealing with the media. See pages 45-47 of the linked document there.
There is one quote I liked very much, "The Sanford city manager shared a mnemonic used by his mayor. He said that in dealing with the media [I would add social media too], one should be Open, Honest, Sincere, Helpful Informative and Truthful (OH-SHIT)." They did not spell out the mnemonic in the document, but I thought it would be helpful to you to do so.
I'm not too sure what the difference is between "honest" and "truthful." I think I'd change it up a bit and make the final T become "Trust." This is what you will engender when you combine all the other elements into your communications.
Not necessarily wanting to "go political" on you, but our current president and his press secretary have destroyed all trust in what they say officially and unofficially by their past lies to the media and to the public. My concern for our nation is what happens when we do have a national or international crisis and we need to hear from these people and get facts and not spin, to know what to do or to define our national collective response or goals. Trust with over half of our nation's population has been destroyed by past deliberate lies. Most recently this was called a "slip of the tongue" that happened on the same subject multiple times. I would not call that a mistake or slip of the tongue.
Once again, a Holdeman quote, "Only you can take away your integrity." Don't ever let someone pressure you to lie. You have a choice!