I did a little bit of research, and if the scratch is toward the edge of the disk and running more tangentially(following the circle) than radially(from the center to the outside) then it makes sense for only a small part of the game to be affected.
The internet research says this:
Make sure that your Wii console doesn't have dust inside that's interfering with play and that the error occurs when the console isn't hot, i.e. you haven't had it on for very long. (You probably knew that but I'm mentioning it just in case.)
If the trouble is definitely with the disk, you can try cleaning it:
Quote:
If the disc is unique and unreadable, then a new draft Standard, ISO/DIS 12024, suggests cleaning using a soft, lintfree cloth and soapy water. The cloth must not contain any particles or hard fibers that could scratch the disc. The cleaning agent must be soap, such as Ivory Liquid; do not use detergents or solvents such as alcohol. Distilled water is best, since tap water may contain impurities that could remain on the disc. Gently wipe the wet cloth in a radial direction, being careful to avoid any pressure on the label surface. Then dry the disc. Do not allow water to remain on the disc.
From the sound of it, trying to repair the scratch yourself is a crap shoot. Practically all of the disc repair guides post a warning about how they're not responsible if you damage your disc even more. There are machines out there that repair disc scratches, and some video game stores have them. You might try calling around to stores in your area to see if they have them and what it costs to get a game restored.
If you decide to go ahead and take the DIY route,
this guide looks pretty good.
"Oh, better far to live and die/Under the brave black flag I fly/Than play a sanctimonious part/With a pirate head and a pirate heart."