package grub-common 2.02~beta2-36ubuntu3.1 failed to install/upgrade: subprocess installed post-installation script returned error exit status 1

The error in your log is:

Setting up grub-common (2.02~beta2-36ubuntu3.1) ...
update-rc.d: warning: start and stop actions are no longer supported; falling back to defaults
insserv: warning: script 'K01.depend.stop' missing LSB tags and overrides
insserv: warning: script 'K01.depend.boot' missing LSB tags and overrides
insserv: warning: script 'K01.depend.start' missing LSB tags and overrides
insserv: There is a loop between service plymouth and urandom if started
insserv: loop involving service urandom at depth 4
insserv: loop involving service hwclock at depth 3
insserv: There is a loop between service .depend.boot and udev if started
insserv: loop involving service udev at depth 1
insserv: There is a loop at service plymouth if started
insserv: Starting .depend.boot depends on plymouth and therefore on system facility `$all' which can not be true!
[...]
insserv: Max recursions depth 99 reached
insserv: loop involving service thermald at depth 1
insserv: Starting .depend.boot depends on plymouth and therefore on system facility `$all' which can not be true!
[...]
insserv: loop involving service mountkernfs at depth 1
insserv: There is a loop at service .depend.boot if started
insserv: Starting .depend.boot depends on plymouth and therefore on system facility `$all' which can not be true!
[...]
insserv: exiting now without changing boot order!
update-rc.d: error: insserv rejected the script header
dpkg: error processing package grub-common (--configure):
 subprocess installed post-installation script returned error exit status 1

This shows that you have some sort of invalid local symlinks called 'K01.depend.stop', 'K01.depend.boot', and 'K01.depend.start' in one or more of the /etc/rc*.d/ directories on your system. These are invalid; the /etc/init.d/.depend.{boot,start,stop} files are configuration information for startpar, *not* init scripts, and creating init script symlinks to them is an error.

You will need to remove these invalid symlinks and re-attempt the upgrade.

This is not a bug in the grub package.

In my case, it was the init.d script for the Samsung Unified Print Driver that was causing the loop. Since the init.d script for that driver is only necessary when using an LPT port, I simply removed the script and the grub installation completed normally.