I recently noticed that some DVD players refuse to play a DVD if part of a recording of it is unreadable (even though you wanted to watch a different recording on the same disc).
Time to check DVD quality: Nero CD-DVD Speed provides scanning and testing functionality, but does not help you in recovering partially damaged files.
I found this blog entry on recovering data files from defective discs, which lists a couple of solutions: Unstoppable Copier, CDCheck, and IsoBuster.
I tried IsoBuster, and as it comes with a zillion options, so I trusted the default values. Once it hit an unreadable sector, it asked whether to replace the sector with zeros or random data, and optionally applies your answer to any subsequent defective sector. I selected zeros, and hope that DVD players are clever enough to handle the zero parts.