The combination of the new sensor in the GH2 and some improved JPEG processing on Panasonic's part has resulted in some of the best image quality we've seen in the company's cameras to date. For example, in most Panasonic cameras--even the good ones, like the LX5--the text in this shot is usually riddled with color noise.
That said, there's still quite a bit of noise in midrange-to-high-ISO JPEG shots; I can't confidently suggest shooting higher than ISO 200 in that case. However, using raw pushes that to about ISO 800, depending upon the scene.
This is the typical color noise pattern we see in Panasonic's images--most noticeably, yellow splotches. On one hand, it's a lot subtler than usual in the lighter shadows. But if you look at the deeper shadows on the left of the photo, you'll see it causes wholesale yellow shifts in white balance.
You can buy about two stops of usability by processing raw files instead of using the JPEGs. You still lose some dynamic range and detail, but even a quick-and-dirty processing in software delivers far better results than Panasonic's internal algorithms. (1/40 sec, f5, Olympus 14-42mm msc lens at 14mm)
The 14-140mm kit lens' geometry looks very good--there's probably some in-camera correction happening, but I don't see any of the artificial-looking straight lines that the correction usually produces.
Despite sufficient light and a low ISO sensitivity setting, you can still see quite a bit of color noise in this photo, which makes the details look mushy. This is another case where the raw version looks great. (1/100, f7.1, ISO 160, 14-140mm lens at 14mm)