Your drive is a POS, most likely a LiteOn. From what I've read, modern LiteOns aren't the best CD burners even at the best of times. I had the same problem with a Liteon/Optiarc.
My suggestion - if you don't want to dump the discs, which I can understand - is to dump the drive and get an NEC/Optiarc, as these are the best all rounders. (By that I mean an Optiarc 7200, 7201, 7203, 7240, 7241 or 7243, as opposed to 7190 and 7220 range drives, which are LiteOn/Optiarcs).
What is your technical skill level in general? Do you understand various disk drive terminologies such as Serial ATA? Would you be comfortable changing your machines DVD drive?
Edit: Although its possible that the discs are the problem, it looks to me like a classic crappy hardware issue.
To be sure though, can you give us the name and model of your CD/DVD and/or model and details of your machine?