Should The New York Times social media editor be tweeting?

In late May, Jennifer Preston became The New York Times ’ first social media editor. She quickly sent a flurry of tweets and then on June 9 her account went silent. The NYTPicker blog illuminated her silence in a post Wednesday, which set off a discussion—including one on Mashable where Preston actually responded —and finally moved Preston to tweet for the first time in one month. The NYTPicker also noted in a separate post  that The Times intern, whose tweet about Preston cau…