I just found a bad DVD+R (TDK 02) in my shelf. It will not be recognized by either Toshiba DVD reader (1612/1712), and 2 of 3 Plextor drives did not recognize it either. The last Plex (712A) can read about 2%, then fails. I've also tried two LiteON DVD burners. They gave up reading somewhere along the way. To cut a long story short, that disk has an average PIE of 1232, an average PIF of 169 and there is one drive in my arsenal which was able to read the entire disk back in. It actually did so at a speed of about 2x on average. As I said, all other drives I've tried would not manage.
The drive that did it was JLMS XJ-HD166s. Amazing little fellow.