Problem:
I get the The "SqlBuildTask" task failed unexpectedly. System.MethodAccessException error when I try and build a solution that as a SSDT project in it.
Solution:
Reinstall the latest version SSDT from here http://go.microsoft.com/fwlink/?LinkID=393521.
Explanation:
I recently built a 2013 Update 4 build machine and none of my projects that included SSDT projects would build. It turned out to be old target files for MSBuild. Not sure how that is possible given this was a clean machine and a new install of Visual Studio. Nevertheless, reinstalling the SSDT bits did the trick.