By errors, do you mean there are inaccuracies in the family history (history errors) or data is missing / broken (computer errors)? Either way, you will probably need to make a new disc. If it's a regular CD (CD-R), then you can't make any changes to that CD ever again. A rewritable CD (CD-RW) can be rewritten, but unless it was formatted with a file system first (very unlikely) then you can only rewrite it if you erase it first. That would cause you to lose everything on the CD, so that option wouldn't work anyway. You will likely need to make another copy with all the changes you want.
By the way, are you referring to a computer program on the CD or just family history data on the CD?