Some comments:

1. It's necessary to insert text into the grep buffer, which is a bit
   concerning because 'compilation-filter-start' is not a marker, just a
   number.  This could cause other filter functions to get confused.
   This is why I'm adding to 'compilation-filter-hook at a higher depth.
   Perhaps there are better approaches here.

2. One could get rid of the awkward first alternative of
   `grep-heading-regexp' if there was a way to distringuish the grep
   process output from the header and footer added by grep-mode.