Dog earing your squeegee channels works very well, makes a big difference, and even though I have been going for an awful long time, that was something I only heard of on these forums. big up the forums!
Agree too about the specialist window cleaning liquids, use them, get used to them, they will make your life so much easier. Even if you don't change your technique in any way it will make your scrims stay dry longer as there is less muck to mop up.
As others are saying on this thread, keep one scrim for your sills, ring it out as it gets wet. If it gets messy then give it a quick rinse in a spare bucket.
Agree too about not washing with your aplicator right up to the edges of the glass, particularly the top one (unless really mucky of course)
My own technique for cleaning a window is as follows:
Wash with applicator, staying a few mill short of the edges if possible.
Wipe squeegee rubber between thumb and forefinger (if you use your scrim for this, all you do is wet the scrim, and with your finger you are also far more sensitive to any particles on the rubber that may affect your squeegee-ing)
Invert the squeegee against one of the pane sides (usually) and the first movement is up to one of the top corners. (this allows the rubber to take up the water to the top edge)
If your technique is tops then you won't even need to 'edge' the window, all you will need is your wet scrim to mop up the water under the bottom edge of the window pane.
Once you get used to using a full sized scrim you will never go back to little cut offs. Trust me on that one.
I have only every used one microfibre cloth, I found it good but also far to small and it soon got to wet to use. Pretty pricey too. But that is just me, a great many on here swear by them, so they must have plenty going for them for so many to enthuse so about them.
Ian