See also: Software
Cannot make directory '/var/run/screen': Permission denied
This issue has been documented here. In short, /etc/rcS.d/S70screen-cleanup is running via upstart much earlier than it expects to have run, and is failing to correctly clean up that directory.
It can be fixed with the following command
sudo /etc/init.d/screen-cleanup start
–Huey
https://superuser.com/questions/1195962/cannot-make-directory-var-run-screen-permission-denied