* I was thinking about giving the tiles "another coat" of grout
this
evening, to cover any bits I may have missed. Worth doing or will I
mess up what I've already done?

Yep, don't worry about going back over, remove some old grout as
necessary. I used some dodgy "adhesive + grout" [in one] from Wickes
once that shrank as it dried, needing a second coat.

Using decent grout (like Bal with Microban) will make the job easier
as
you only need to do it once.

It's quite important to ensure you have to go over the grout line
only
once as it's a bad enough job as it is, without doing it twice .. !

OP here.
Its been 2 days since I did the grouting. There is a fine layer of
grout on most of the tiles. How do I remove this...wipe over with a
damp cloth?

Bruce