The surface is treated with a special cover that helps against glare and s"starbrights". Basiclly, it helps to control the bleeding of color onto other dots. There 1000s of dots that make up a monitor. Since most monitors are non-interlaced (the oppisite of a TV) the dots are perfect and run across each other. That's why a computer monitor is much more crisp then a TV. The coating on your screen affects the amount of color bleeding and glare.
Bottom line...WINDEX...WRONG. Yes, you can damage your monitor when it come to quality of picture.
To clean a monitor use special monitor cloths that you can get in a computer store. Or do what I do and use a VERY soft rag (not paper towels) warm slightly soapy water (I use baby soap) and clean. To dry I take a VERY soft dry rag and wipe until all streaks and mositure are gone.