This question is no longer relevant now that Panasonic has introduced new features into the GH4 and subsequent cameras’ firmware.
Vitaliy Kiselev managed to dissect the GH2 (and GH1 for that matter) firmware and figure out how to use it to have the camera's built-in image processor use different settings than are revealed through the usual menu system. You can find out more about his firmware hack here. Currently, some people managed to get 176Mbps streams out of the GH2 successfully. That compares with the more usual 25Mbps rendered by conventional AVCHD compression cameras like the GH2 typically maxed out at the time. More bits per second means less compression is going on, which has impacts on the clarity of motion and rendering of fine detail.
So why didn't Panasonic just do this themselves? First, AVCHD is a standard centered around Blu-Ray discs. The implication is that Panasonic picked something that they could guarantee you could record to Blu-Ray. Given that was about the highest density recording medium accessible to most people at the time, the decision made some sense. Beyond that setting, as you kick up the bitstream speed issues of tolerances start to come up. The card you have might not actually support that much data coming at it, for example. Thus, I suspect that Panasonic simply picked some reasonable and conservative settings for the compression engine that would guarantee no dropped bits/frames/data.
If you try the hack, do plenty of testing of the exact settings you're going to use before relying upon it. Make sure that your camera and card are compatible with the settings you choose, and test the compressed stream with your video editor. On the flip side, if you're deep into video and have a GH2, there's almost no down side to trying the hack (as long as you pay really close attention to the instructions) as I've seen almost everyone be able to find settings that record better quality video (less compressed data) from their camera/card combination.
