How to Fix a Scratch on an LCD Screen

Use Vaseline petroleum jelly to fill a scratch on an LCD screen. This works because the optical density more closely matches the LCD face than air.
Steps
1. Clean the surface of the screen.
2. Take some Vaseline and fill the scratch with it.
3. Gently wipe off the excess Vaseline, being careful not to press too deeply so as to leave some inside the scratch.

I find WD-40 to work exceptionally well. For deep scratches I use WD-40 and a brand new razor blade to skim the excess off of the scratch. Then apply liberal amounts of wd-40 to a non scented tissue and and rub it into the surface. It makes the screen look cleaner and brighter. The only draw back is an abundance of dust afterwards.

I used the following method when I knocked over a brand new 22" LCD display onto a pen sitting in a cup, putting a noticeable 6-inch long scar in the surface of the monitor. I ran out to my car and got some fine grade rubbing compound and a clean cotton rag. I squirted a quarter-sized glop of it into the cloth and rubbed across the scratch and a couple of inches on either side of it vigorously, easing off the pressure as I got farther from the scratch. Then I wiped off the compound with a clean part of the rag. It took about three applications to erase the scratch completely, and then I polished the entire screen with a clean and dry soft towel. The display functioned perfectly and looked good as new.