You might initially try to rinse with the brush on the glass after you have scrubbed it. You do this by just tickling the bristles of the brush on the glass and slowly weaving it down side to side to the bottom. This should bring those little bits down as well. Then do a second rinse with the brush off the glass and see what happens.
If you see the odd bit of grit after that leave the window to dry down, but make a point of going back to check it later, being prepared to redo if necessary. This will help you to identify what to you can safely get away with and will help you gain confidence. No matter how much you try, you will never get the window 100% perfect, but your aim should be to get to as near perfect as possible without spending all day doing it. On the other hand, if your customer suffers from cleaning OCD then leave them to the next cleaner to find out about.
We usually clean the next house and go back to the first to wipe the cills down, and use that time to give the windows a quick scan. Good thing we do as I have missed a couple of windows accidently these last few weeks.
Spruce