Rolling shutter artefacts are typically identified when panning quickly during video recording. This can lead to "wobbly" effects, square objects can be seen to lean towards one side.
To compare these artefacts again between the GH2 and GH3, I mounted both cameras to a piece of wood:
I used Manfrotto Superclamps with ball heads to fix the cameras to the piece of wood. These are quite useful.
On the GH3, I put the Lumix G 14mm f/2.5, and on the GH2, I put the Lumix G 14-42mm f/3.5-5.6 kit zoom lens.
The latter zoom lens, used on the GH2, was not set to 14mm, as you might expect, but rather to 16mm. The reason for this is the lack of the multi aspect sensor on the GH3. So to match the video field of view of the GH3 at 14mm, the GH2 zoom lens must be set to around 15-16mm. Read more about the multi aspect sensor here, and also how the lack of this feature affects the GH3.
After having mounted both cameras to the plank, I set them to ISO 400, f/5, and recorded video as I panned them simultaneously in front of some buildings. Here is the result, where I have used the left part of the frame from both cameras. Note that due to the wide angle used, there is a bit of perspective skewness as well to the video:
We see that when panning quickly, the buildings appear to lean a bit to the side. Here are some screen shots from the video:
When panning left:
When panning right:
The differences here are quite subtle. There are visible rolling shutter artefacts when using both cameras. In general, I think the footage coming from the GH3 shows somewhat more similarity between the stationary footage, and the panning footage. But in terms of rolling shutter artefacts, there is not too much difference.
Keep in mind that the panning here was quite extreme. You would rarely pan this fast in reality. So for most uses, the rolling shutter artefacts using any of the cameras is no problem at all.
When using the electronic shutter mode of the Panasonic GH3, though, there is significantly more artefacts coming from the slow sensor readout.
Note that this was not done to compare the video quality between the cameras. I selected quite low bitrate on both, to avoid bogging down my hard drive with large files. That said, I think the GH3 does better in terms of auto white balance.