Federalevidence.com has this piece on about juries and social media, and a discussion of the model jury instruction.
They also link to an interesting 22 November 2011 Federal Judicial Center report .
The use of social media by jurors during trials and deliberations is not a common occurrence. Of the 508 judges who responded to the survey, only 30 judges (6%) reported any detected instances of jurors using social media during trial and deliberation[.]
Of course in civilian court it wouldn’t be an Article 92, UCMJ, violation.