Older models do, newer ones do not because they are much more resistant to burn-in. Destinys HUD is just very, very bright and has no opacity, it's completely solid.
Mind you, LCDs and LEDs also can get burn-in. This isn't just plasmas. It will take longer, but it'll effect other type of sets other than plasmas also.
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Ah. I wanted to get a nice LED but they were out of my price range. Ended up going the Projector route because I found a great one for less than half of what it normally sells for. Biggest selling point for me was easily replaceable bulb