Barb wrote:

Well my new lawn, laid by the builders a few weeks ago, is doing ok and now
needs its first light mowing. I've taken care of it, watering, etc.

However, it was not particularly well done - a bit lumpy - and there are
gaps between some of the pieces, which I don't think will fill spontaneously
over time.

What's the best thing to do about these? Fill with compost, tamped down
well and seeded?

How big are these gaps? A 50:50 mix of topsoil and sharp sand ought to
be OK for filling in small gaps. And unless the gaps are really huge
grass will spread to cover any gaps pretty quickly once it gets going.

Chances are you be able to see the lines of whatever new grass seed you
introduce to the bare patch unless you very carefully match it to the
turf type originally used. I have a visible patch of "new" grass that is
slightly nicer green and better texture than the main lawn where a pear
tree used to stand. It is still obviously other grass five years later!

Regards,
Martin Brown