use cdck to tell if an old CD-RW should be thrown away
 

Based on a tip from someone here, I have found out that I can determine the viability of a CD-RW with a program called "cdck." It read all the sectors on the disc and let me know that a large number of them were unreadable due to I/O errors. It runs in the console; I had to go there and type cdck because it didn't put itself in the launch menu.