I found a published paper that looks dodgy. What to do? I looked into an article published rather widely in the media, but on a fairly marginal topic (perceptions of grammar use), so noone will die or ever bother to replicate or correct it.

The contents of the paper looked dodgy in analysis and setup, but more than anything else, the statistics look very suspicious and possibly erronous or at least probably mistaken in assumptions. I contacted the corresponding author for their data, and their editor for an overview of their data sharing policies. No answer from either for more than a month.

What can I do? Is there maybe an online web-environment, where I could flag potentially dodgy studies for further discussion? If the contents are as dodgy, what leverage is usually in process for a retraction to happen? Thanks!

The question is about this particular paper, but this kind of thing can come up a lot. If this was a paper in my own specific area of interest, I would maybe write a public answer, but as this is not, I'd just point it out to other interested parties.
A good way of posting comments, anonymously or not, with a good chance that other people will read them and react is Pubpeer. Although not all fields are covered, you can post your criticism on many articles. Sometimes authors react, sometimes publishers take action, sometimes nothing happens. 


  what leverage is usually in process for a retraction to happen?


A good list of the cases where Pubpeer comments lead to retraction can be found on the Retraction Watch website:

http://retractionwatch.com/?s=pubpeer