The only way a disc can be scratched the way you describe is if you moved your console when it was running. Did BestBuy replace your copy? Your lucky if they did.
I recently purchased and was playing Gears of War and when one of my friends was going to start a solo game, the system told him that the game was dirty or something. When I took the game out of the system, I saw that it was completely scratched all the way around (in a circle) the disc. I went to Best Buy to exchange it and I found another person there exchanging a game (NBA 2007) with the same problem. Is this a common problem with the 360?