Unfortunately there were some scratches on the surface of the LCD display screen of my Dodge Charger's radio right out of the show room when I bought it.
LCD screens are very sensitive, and should NEVER be wiped with a paper towel, napkin, or even terry cloth. These types of material are way too harsh, and if there is as little as one grain of sand or dust particle as you wipe, you might as well use a Brillo pad, it will permanently mar the surface just the same. Once they are in there, they are permanent.
I am not aware of any products that will safely, and satisfactorily buff out scratches on an LCD screen. However, I have been told there are some home remedies, and products on the market*. I have not tried any of them, but came up with a different fix... Then again, fix isn't the right word here, it's more of a clever patch-up...
1.) Buy a pack of display protectors for BlackBerry phones and PDAs... (Verizon store, $9.90)
2.) Get a piece of white paper, a pen or pencil, and a pair of scissors.
That's all you need!

Take the sheet of paper and get an imprint of the LCD window. All you have to do is hold the paper perfectly in place with one hand, and rub it it with your other hand (thumb) to create an imprint mold.


Trace the pattern with a pen. You can use the screen protector cardboard package insert as a ruler to keep your lines straight.

Measure the screen length and width on grid, then trim the grid to screen size.


Wipe the LCD display screen with the the special dry cloth that was included in the display protectors package to remove oil, or dust. Peel the corner away from the grid backing, being careful not to touch the sticky surface of the LCD protectant foil (you don't want finger prints or lint on there!). Hold the display protector from the corners while applying to LCD using the handy little plastic smoothing card that also came in the pack.


Try to position the strip right from the beginning, as it makes the application a lot easier. However, you CAN reposition the protectant film by gently lifting and reapplying it, if necessary.
And PRESTO, here is your new, scratch free LCD screen.
*Final remarks:
I have heard about a product called CD 2000 that buffs scratches out of plastic, and it may work for lighter scratches. Someone else suggested using toothpaste, soft pencil eraser, or Brasso. I never gave these suggestions a try as I don't know whether it may actually worsen the problem. I feel using the screen protector film is a better solution, and more beneficial, since it also protects the screen from more scratches.