If the errors happened only on the real Saturn, the Saturn itself would be the problem, but if an error manages to happen in your PC CD-ROM (that I suppose is a bit new, and good quality - cheap CD drives will do you no good), then the CD is the problem, and you won't be able to make a copy out of it. Maybe the only way before downloading a backup, or buying a new copy, is trying to resurface the disc.
It may not be scratched, but it can be damaged in other ways. A very common way to screw a CD is to have it receive direct sunlight for some time (like, your CD deck gets hit by some sunlight during a certain time of the day). I lost a bunch DC backups that way (thanks god they were backups). The CDs have no visible strains, but the DC will not read them properly anymore. Some other envronmental conditions can also mess up a CD. The CD plastic itself might suffered a change over time, depending on what it has been through, and that makes it harder to read, and SFIII in particular is a pricky game when it comes to CD integrity - the game will halt on the slightest error. Nights, as example, runs under the worst conditions.
I got a heavly damaged Nights CD, and it takes AGES to load on the Saturn (the level loading sequence gets so screwed when the load time takes longer than expected), and the FMVs are a history, but the game keeps trying and trying, until it finally loads the darn levels.