I must have misread. If the game runs, you won't get a disc error any time soon. Seriously, the only time the game won't run is if you treat the game like shit and kick it around and everything. As long as you take care of it, the game won't break. Unless, it's seriously gashed, etc.. then it probably won't work.
I don't see why you would be worried about this, as mostly everyone treats their games with some decency, especially if its a newly released game. Unless it's a rental, then most people don't take care of it very well.
Audio CDs and Games are very different. Whenever you take bad care of your audio CD, the music on there will become scratchy, staticy, and unplayable -- most likely, you pirated the music, and treat the CD like shit because you didn't pay anything for it. As for Xbox360 games, the chances are you didn't pirate the game, and will probably care for it better.
As for testing the Xbox360 game, I guess you can test it at a friends' house or something? This question practically answers itself because its mainly common sense. As for the game company you traded it to or whatever, it's their trading policy/warranty thing. If the game doesn't work, then go complain -- that's what its there for. There's no need to be paranoid about this shit if they have it covered, no?
If you aren't going to play it for a couple weeks, at least run it first whenever you get it and see if it runs or not. If it doesn't go return it and ask for a new one. Don't wait until a couple weeks later when you're going to run it, find out it's broken, be like OMGWTF!!! try and return it and they're like, well, you got it like 3 weeks ago, how do we know you didn't damage it? If you return it the day after since it didn't work, they'll believe you.