What to do if authors don't respond to my serious concerns about their paper?
Write a response. (Would such a thing get published?)
  


This. Such things are usually titled "Comment to..." and, yes, they are published, typically alongside with a reply from the authors of the commented paper (the comment is usually sent to them by the journal editor).

As usual disclaimer, since things may vary across fields and journals, check if the journal in question has already published comments of this type and, in doubt, contact the editor.