The people on MyCE (better known by their old name CDFreaks) usually use Nero CD-DVD Speed. The version I have is 126.96.36.199, but I don't remember if there's any particular reason I downloaded that version.
The "disc quality" test in that program doesn't access files, it just reads through the whole disc and counts/graphs the number of low level errors that were reported by the drive. If the drive supports it, then it will also measure jitter, which if I'm not mistaken is the degree of nonlinearity in the spacing of the bits on disc.
It will report a simplified "Quality score" at the end.
Having errors evenly distributed through the disc is better than having them clustered. I think the "quality score" is based heavily on how densely the errors appear in one spot of the disc. The "maximum" C1/PIE and C2/PIF values that are shown for the Quality test are the number of those error types that appeared in the same vicinity. If I'm not mistaken that "vicinity" is a single error-corrected block ("block" is probably not the right term).
The "maximum" C2 or PIF value is the most critical. On a CD, I think only C1 errors are correctable and C2 errors are unacceptable, but I might be wrong. On a DVD, both levels of error are correctable but C2/PIF are more serious.
As mentioned, the results will vary significantly depending on the particular drive that you use. People on MyCE like to use one of a few widely accepted drives for doing quality scans, so that they can compare results with each other on the same models of drive.
Some people have argued that the best test is to simply perform the "benchmark" test, which graphs the linear transfer rate as you move across the disc. A good disc will show a smoothly increasing transfer rate. If the drive has problems reading something, it will cause a hiccup in the graph.
The biggest problem is that you can't really test the discs using the same drive that's in the Playstation console. The drive in your PC might like a disc better than the Playstation does. But still, you can get a general sense of when one disc is probably in better condition than another.
These tests can also be useful for checking the quality of burned CDR/DVDR discs. For example, I found that a newer batch of blank DVDs didn't work well at all with my old model burner. They worked but a quality scan showed that they had not been burned well. The problem was apparently the drive's firmware predates that particular MID code of discs. Presumably a disc with lots of low level errors is not going to last as long in a readable state.