GH2 lens question: How is sharpness affeted in video?

Don't know if this is the reply you are looking for, but many filmmakers like to use legacy lenses, with an appropriate adapter of course, to use with the GH2, precisely because these can give a softer, more filmlc look than the modern lenses made for the camera. Regarding your comments about pixel binning, the GH2 is famous for the way it does this as compared to other large sensor cameras, minimising artifacts to give a highly detailed 1080p picture. A good resource for further reading about these matters is eoshd.com. The websites publisher Andrew Reid has also written a downloadable book about the GH2 - the Shooters Guide - which covers all aspects of its use for video, including lens choice. It costs a few dollars.