I'd try some here for $5.00
Several readers, both from the Netherlands, write that Brasso metal polish works great for polishing scratches and wear out of both compact cameras with worn screens as well as saving $20 on having to replace the replaceable LCD covers on cameras like the D1, D70 and etc.
I personally haven't tried it, and it makes perfect sense. If I had this problem I'd get some here for $5.00 and try it carefully.
I have tried both Meguire's Plastex as well as plastic countertop polish. They worked, but weren't very strong. At least they improved things and didn't make it any worse! You'll have to work at it for a little while.
Caution: this is only for plastic covered LCDs. DO NOT use it on glass LCDs. Many compact cameras have no protective plastic and have the glass of the LCD exposed. I don't know what would happen, but using this polish on the specially coated and finished glass would be asking for trouble! Use polish only when the glass LCD is protected by plastic. It's the soft plastic you can polish, not glass.
Also be careful not to get any of the dried dust anyplace. Be careful, for all I know you could screw things up.
After I posted this a mechanical engineer reader, Bob Martin, writes that Brasso is problematic due to it's low viscosity and reactive content, especially if it gets where it doesn't belong. (You can see Bob's animation website here.) He's used two products to refinish plastic lenses and other optical surfaces for many years with great success.
They are Simichrome Polish, sold in motorcycle stores or you can get it here, for polishing aluminum to SIMIulate (sic) CHROME. The second is Blue Magic, a competitive brand to Simichrome, sold in antique stores or you can get it here, for polishing metals. He became convinced of their usefulness when he had a modelmaker friend use Simichrome to polish the anti-reflection coating from his pair of glasses without distorting the optical characteristics of the plastic lenses to which the coating was applied. Both products have the consistency of toothpaste, smell less than Brasso and can be very easily applied and polished with the "original" polishers: your fingers.
Of course toothpaste also has a fine polish in it, and I personally use toothpaste to polish small blemishes from friend's automobile finishes when I'm too lazy to find my proper polishing compound!