I had th same error i dawnloaded a game an i can play it but in the midlle of the game makes the error There's a problem with the disk you are using. It may be dirty or damaged. please replay
it is most likely your xbox dvd drive...they are very picky and don't like burnt media...some backups will work flawlessly and others will just be a pain in the ass.
Your best bet is to replace the HDD and store games on there. Besides a few that need patching, it works for all games, even the dual-layered games.
I found a way to burn it a the error dont apear at all you have to burn it with nero express and put the speed at 4x im not an expert but it woked for me