Which part of blue fish is not edible?
From Fishing Tips: How to Catch, Prepare, and Cook Bluefish:


  When you clean the fish, remove the skin and any dark-colored flesh. This part of the fish is especially strong tasting and somewhat oily.
  Check out these fish recipes to learn to cook bluefish.


Also see How Can You Cook Bluefish To Make It Taste Good for advices on improving the flavor (e.g. soak it in milk).