A few years ago I found a quick fix that lasts a long time. We purchased a new LCD and set it on a low table only to have our dog immediately jump at the screen and drag is nails across half of the screen, leaving deep scratches. I then took a soft cotton cloth (a cloth diaper) and wiped it back and forth across the scratch (sideways, not lengthwise) until the scratch disappeared. I haven't seen any trace of the scratch since the initial application, even after cleaning the screen with the blue spray stuff every month or two for the past 5 years.
RyanY, February 2013