STOP! no plege, no windex. Use a product that is safe for non-glare coatings- I use/recommend this:
http://www.touchofpurple.com/
in a pinch, pick up some distilled water at the local phamacy, put it in a CLEAN spray bottle, and add a drop of dish washing soap.
Get a good micro fiber cleaning cloth ( Ilike the blue ones from 3M) and keep it clean, and use that.
The screens on current 'daylight' veiwable units are very touchy, and just swiping some spray off with your shirt sleeve will ruin them-