So, if your Xbox 360 console has problems in reading the disk, it might be because the disc is dirty or damaged or the hardware has problems. This is what you could try doing to fix it:
1) Turn console off and then on again.
2)Clean the disc and examine the disc for flaws or scratches.
3) Delete the appropriate saved games (because, if a saved game file is corrupted, it can produce a disk error message in that game)
4)Try three other games and then try the original game again.
5)Try the game on another console if you can.
6)Replace the disc at retailer.
If none of these possible solutions solve your problem, your Xbox 360 console might need to be serviced. If that’s the case, contact Microsoft and send your console for repairs.