There is still an issue I'm aware of: if one saves a grep buffer to a
file and later opens the file, the headings are inserted a second time.
I've tried a bit to display the headings only using text display
properties (instead of inserting the actual text into the buffer), but
wasn't successful so far.  Other, less elegant solutions are possible
(e.g. deleting all headings either when saving or when reading again the
file).

We could install this change now and polish it later or continue this
discussion -- both are fine by me.