Well, I'm not the only one who has wondered this question. And I just happen to have quite a few CD-R's and DVD-R's that I burned in the early 2000's that I can do some quick tests on.
First example is a super cheap CD-R burned for me by Rob DiNapoli at CGE back in 2000. This thing is so cheap that the disc is transparent. Incredibly, it still was readable (at least, I think it is, I didn't actually try copying the file off the hard drive) but as you can see it has some problems toward the end of the disc.
Next is one of the first DVD-R's that I ever burned, back in 2002. This is a TDK with no speed rating (1X?). As you can see, the TDK has trouble at the end of the disc. Is the disc still fully readable? Yes it is, I just copied all the files off of it onto my hard drive without problems.
Finally, here is a Memorex (!!) that I burned in 2003. Lest you think Memorex is good, let me assure that I have lost entire Memorex DVD's where I could not even read a file system. I will never buy Memorex again. Still it's nice to see that some of them can last for 10 years. Note that I did not fill the whole disc; if I had there may have been massive errors at the end.
Conclusion: It seems that the end of the disc tends to go bad a lot. For this reason, I always fill 10% of my burned discs with .PAR2 files so that I can recover from bad sectors.