High frequency low voltage digital signals can already be a pain, so imagine what high frequency HV digital signals do...
I never liked Plasma TVs. Expensive, power hungry, noisy, shitty contrast, and screen burn in... Fortunately large LCDs came before I could afford one anyway
Actually, plasma TVs have really good contrast and much richer blacks compared to LCDs. All in all, if you compare an equivalent size LCD and plasma set of the same time period, the plasma will always have a better picture.
This comes at the cost of heat, power consumption and weight (as you mentioned). Burnin is also a very real issue (my parents have a 10 year old set that has a certain cable news network's logo box and ticker permanently burnt into the bottom of the screen, courtesy of my father).
On the upside, modern plasma burnin isn't like old monochrome CRTs (or early "orange plasma" displays used on Toshiba and Compaq transportable computers) where the actual text literally burnt into the screen. On plasma TVs it's more like a faint pink "smear" in the general shape of the image, and it's only really visible on a solid white background.
All that said, my plasma set has lasted 10 years with no issues. I'm overall very happy with it. It's held up a lot better than any LCD of similar vintage that I know of. It's a shame they didn't keep developing the technology further, but I guess you can't compete with the cost/performance ratio of an LCD!