I have just tried some microfibre cloths, they are top quality unger ones for glass (you can get thicker rougher ones for the sills etc) its important to get the right ones if you want to use them for just the glass, the cloth is much finer than normal microfibre. I only went for the smaller size, so any wet bit doeasnt dangle down onto the window - you can buy then in packs of ten if you want to.
I will still be using my scrim to wipe down the upvc and sills etc and to wipe away most of the water round the edge of the window. For the finer detailing, just the bit that may be left on the edges of the glass, i just use these to wipe round the outside edge - just finger width. I find they get rid of any slight bemishes on the glass, where the old scrim might leave a slight trail. Either way you have to keep them really dry and clean and just use them round the edges of the window/glass.
Steve