I have had my GH2 for 3 1/2 months and I have not seen one instance of posterization. Maybe it exists in your camera, or maybe not. There are so many variables that come into play - how the picture is being decoded on your computer, what software is displaying it, the graphics card or chip and it's settings, even the computer monitor itself. Any one of these could be the cause.
To cut through all this muck, do this simple test. Take an HDMI cable and plug your GH2 directly into a TV. Play a clip that you think has posterization, from the SD card in the camera . If posterization appears on the TV, then it's for real. If not, then the problem is somewhere in your computer's "food chain".
Thanks for the advice. I'll try to plug the camera directly into the TV just to be sure. But the thing is that in the first two months with my GH2 using mostly the 20mm pancake and a Canon FD 50 1.4 I failed to notice any instance of posterization (not that I was looking for it). The moment the Voigtlander 0.95 arrived I made a quick first video with extreme close shots of a bunch of toys and the lens wide open and there it was, posterization galore. From then on, I started to see the nasty effect in other places though most of the time is so subtle it doesn't bother me that much. So it can take a while to notice posterization in GH2 shots and depending on the kind of work you do, you may never notice it (well, most probably you'll do sooner or later).
The GH2 is a great camera, don't get me wrong but I still think that Panasonic should figure a better way to deal with potential posterization. I mean, far worse cameras have done a better job to hide posterization in the past, it's ridiculous that the GH2 can't do it. The overall quality of the image is so amazing that this effect stands out even more, like it was pasted over the image.