If you are like me you probably have searched for clues to and found little... particularly when confronted by the errors as you unravel how this works. Okay a slight exaggeration, there are snipets of info that people have solved this annoying issue in making comments work in Drupal 8 REST services.
The lack of collective information in resolving issues has meant hours of debugging and working through core code to understand what is actually happening. If you want to read more on how we got the comments working in REST - goto Drupal 8 REST POST comments.
415 Unsupported Media Type
Then most likely reason for this error is the Content-Type is set to application/json rather than Content-Type being set to application/hal+json
Change: Content-Type: application/hal+json