Here's a video shot handheld at an exhibition recently.
For this I used the GX7 and the Panasonic 14-45mm kit lens.
I've had the kit lens for years but this is the first time I'm using it. Never gotten around to selling it, but it proved to be very useful.
I had lent my friend the Panasonic 12-35mm and it's still not back yet. The 12mm is more useful indoors. The 14-45mm is the only other lens with image stabilization.
OIS is extremely useful when shooting handheld. Without it, I've no doubt most of the footage would be more jerky, especially towards the 45mm end.
The 14-45mm performed very well, in terms of clarity of the video. It was shot in 1080P. The noise performance is also quite good, noting that this lens actually starts at f/3.5.
I've turned off Autofocus during video mode, choosing instead to focus by half-pressing the shutter. Sometimes it's fast, sometimes not, but generally speaking it's acceptable. On hindsight, I should have practiced with manual focusing.