This seems like a pretty straightforward thing to identify. I remember when the NYT's story, "The Agency", was published [0], some of the fake accounts it had mentioned were still up. Even though the accounts in that story were actually populated by real people, the sockpuppetry was pretty easy to identify. One: the accounts' past tweets right up until they started spreading the news about the fake U.S. disaster were in Russian. Two, all of the tweets of the fake news had almost exactly the same number of favorites and retweets (around 300), and you could see that everyone in that cluster was just retweeting each other.
I'm more fascinated by the spam by Facebook accounts. These show up all the time in relatively popular comment sections, and yet apparently FB doesn't care, or the problem is trickier to automatically flag. For example, this comment [1] is clearly spam...but if you click through to the account, it seems to be a real person [1], with a normal-seemingly friend network, mundane photos of life that aren't obviously stock photography. There are a few junk comments (a bunch of "hi's", but as an outsider, this is what makes FB a lot trickier to analyze, because you don't know how much privacy that user has enabled on their own account.
[0] https://www.nytimes.com/2015/06/07/magazine/the-agency.html