Here is a dance I shot Saturday using the gh3 and 35-100 (2.8, 500 ISP, 30fps, 1/60).
It is slightly over exposed and I will correct and grade later, but I was amazed at the quality of the autofocus tracking as this dancer moved around the stage. This cam was a B cam to another gh3 so I felt fine using auto focus.
First time using auto focus and it ALMOST makes me want to switch to auto during bright ceremonies!

GH3 35-100 AutoFocus Test on Vimeo

As a side note, can anyone tell me about the banding in the background? What causes this? Is there a way to avoid it?

Yes it handled it very well and your manual zooming was pretty smooth as well. Props. Were you just holding the camera itself or were you using any kind of a rig?

Great lens, skilled shooter, well done.

Thank you for the kind compliments. My intention was only to show how great this AutoFocus worked.
I am left handed, so I had this camera on a Manfrotto tripod with the stick in my right hand and my left hand (dominant) on the zoom ring. I have found that a professional tripod set of stix and head can mean more for your video than many other accessories. Certainly made this contant camera work easier! I also had middle-back wide camera recording when I did screw up :)