Having black bars on any source that is not 1.78:1 or 16:9 (same thing) is very normal. All HDTVs (LCD, DLP, Plasma, etc...) have a native 16:9 aspect ratio so if you watch anything that doesn't match this aspect ratio you will get those black bars. If these black bars really bug you most displays will stretch a picture to fit the full screen (sometimes slightly cropping the image). While some people like stretching the image, it drives me nuts as you can see that the people are stretched. I suggest that you play with the settings to see if you mind images being stretched or not.
As far as burn-in goes I wouldn't worry about it. Burn in is permanent and with your plasma would take
a lot longer than one movie to cause. Rather you are seeing something that LCDs are also subject to called polarization. This is when pixels are displayed for a while and then get temporarily locked in their position this problem is very easy to fix all you have to do is watch some HDTV and the pixels will regain proper function
.