PL2 - Did I Get a Bad One?

You can probably get rid of the stuck pixels by remapping them. Menu, Gears, J (Utility), Pixel Mapping.

There's a lot of noise in the shadow. Do you have the camera's noise filter turned off? Menu, Gears, G. I have Noise Reduction Auto, Noise Filter Low. A higher setting for the filter might be better for you in low light. If you can't get better noise reduction, I'd say the camera has a problem.