On my old diamondtron 22" CRT I use a damp paper towel and make tiny tiny circles(think Karate kid

)rubbing on every spot till it dissolves, after that I use a dry one and repeat the process, just wiping it in straight lines seems to always leave smears which you can avoid with the circle technique.
Know people say you shouldn't use Paper but paper towels seem to leave no dust behind(unlike "professional" antistatic cloth) and I don't press anywhere near hard enough to make scratches.
Also use water instead of monitor products as they seem to always leave a shiny film behind and leave ugly stripes all too often.
Same technique works wonders on our large LCD TV (though it does take up to 30minutes to do it properly thanks to greasy kiddie fingers and it's size) and the TFT on the work pc.
Think I clean this monitor about twice a week as the small specs turn into a real PITA flying with forced cockpit and icons off.
Have a feeling us WW1/WW2 flightsimmers are pretty much the most OCD about clean monitors of all gamers lol.