I had a similar issue with vBrawl before. Based on my personal experience with it, it potentially could be the disc.
While the scratch may not be large or deep, it may be placed in a critical area for a certain character to appear. For example, my scratches were made exactly where the characters Wario and Young Link were. While I was able to play the game just fine 90% of the time, whenever I tried to load a match with either one of these two characters, my game would freeze.
An easy way to know if this is certainly the problem, and not just an installation issue, is to try to re-download re-install project M. If this works then no more worries. If not, try this second step
load brawl normally, go into the multiplayer brawl menu and select each character in the menu, one second at a time (do not start the match). In other words, load the menu, select Mario for 1 second, then unselect him and then select DK for 1 second, then unselect him and then select Link, etc etc. if at anytime your game freezes, then, like me, you have a character who was scratched out and you'll need to repair/replace the disc. If not, then I don't know what it may be.
