Both have their share of problems, but as you might have guessed by the pricetags Plasma has more PROs than CONs.
LCD suffers from bad black levels and "white crush" due to having a backlight. Also suffers from ghosting in video games and 99% of LCDs only support 1280x720 or 720p as their highest resolution.
Plasmas only downside is the gas inside the panel cannot be replaced and alot of people are finding out after 4 years or so their $5-20k plasmas are not under warranty and the gas needs replacing. There are a few 1920x1080 or 1080p plasmas but they are 15k+, most high end consumer grade models still max at 1280x720 and some 1388x768.
DLP on the other hand has none of these problems except for stuck mirrors sometimes, but should be covered under warranty. You can get a 1080p 70" one for around $6000, compared to 15k+ for a LCD or plasma that size and 1080p. They weigh more and are thicker but not too bad, about 1ft thick and 100lb for the 70".
IMO TV technologies go in this order as far as picture quality. LCD<Plasma<CRT<DLP. And in the bang for the buck category its Plasma<LCD<DLP<CRT. I don't understand why people are so concerned with a tv being thin, I have a 300lb rear projection widescreen and I move it once a year, TOPS and for $1000 I have a 57" that competes with DLP/Plasma etc... on picture quality, LCD is a waste if you plan to watch any movies, simply terrible.