The books stress having the slab flat, grinding the high spots and
filling the low ones. But just how flat does it really have to be? Can't
I just use a little thicker layer of mortar to fill the known low spots
as I lay the tiles, especially if I "beat" the tiles into the mortar to
assure good contact as some books recommend?

Some books and websites also stress the importance of a level slab.
What's so bad about it not being level to within 1/4" per 10 feet?

My slab is at grade.

Thanks,

Ray