Well the Samsung s203b and others can do quality checks, but not jitter, the liteon's should do all checks, and BenQ's older drives like the 1620, 1640, 1655 do nicely. I'm sure there are some others but those are the main players I know about. I use my BenQ drives here to do my checks but they are no longer available new easily, though used and new ones show up from time to time on Ebay.
Plextors do it of course, and I'm pretty sure the newest Sony/NEC drives do as well. I think they all sound about the same, some drives have issues recording cdr's but most newer drives should work fine. If your talking about noise they are all a bit noisy when burning a dvd at full speed, most are a lot quieter when just playing back a disk. Look at the reviews here, if a drive is really noisy it should be noted.
Well, a lot do it but they aren't very accurate. If you can find them, your best bet is one of the BenQ drives Dartman mentioned or one of Plextor's older DVD writers.
Plextor's new DVD writers can also do write quality testing but they're essentially rebadged Lite-On's.