This wasn't for this past Christmas, but a few years ago my brother gave me a handy dandy CD scratch removal and cleaning machine. I think it was sold in the Sharper Image catalog, and also available in ominous colorful piles by the checkouts of your finer department stores. It was a plastic clamshell device with an AC adapter and a bottle of magic cleaning fluid. It came with two different grades of polishing wheels. It claimed to make scratches on the CD playing surface disappear. I found myself one test CD, that I'd obviously loaned to someone and was returned with a few scratches. I first used the finer of the two cleaning rings and a recommended amount of the fluid. Well, I can say if you don't like seeing a reflection of yourself, or those pretty rainbows in the back of the CD, this gizmo is definitley for you! It basically takes some mild grit polishing compound, spins it agressively against the playing surface of the CD and takes the plastic down to a dull haze, leaving previous scratches still clearly visible by the way. I tried the more coarse cleaning wheel. More of the same, but even less recognizable as a CD. Scratches still there. It still played but now skipped more than it ever did. I tossed the CD. I'm hoping that I saved the machine somewhere so I can try spreading it on my lawn as Albert suggested.
Marco