Some lenses will have a "ghost flare" when wide open, but it has more to do with the lens than it does the camera. I don't think the GH2 is creating that artifact, but rather the glass (and would happen on just about any body). Stopping it down a notch or two usually helps eliminate flaring, but some people like the look.
I've worked on music video / concert footage where the producer actually LOVED the flaring and asked me to do it more often. Some hollywood flicks shoot with flare-heavy anamorphic lenses on purpose for style (Transformers, Blade Runner, the recent Star Trek, etc).
If you don't like it, try a different lens, use a lens hood and stop down your aperture a bit.
What lens are you using on your GH2? Does it have any kind of UV filter screwed onto the front? If so, that could be causing the ghosting. If so, try removing the filter. On the second video, that just looks like classic lens flare. It's normal, and like the previous poster said, some people do it on purpose because it looks cool.
I shot the second video and in it I used a 7d for the closer stuff and a GH2 for the wide shot. The lens on the GH2 was a Canon EF 28mm 1.8 lens with no uv filter. I want to say the video with the fire is a Sigma 30mm 1.4 EF-S lens.
Looks like normal flare to me. Some lenses have milky, beautiful flare with little ghosting, and some look like garbage the minute you point them at a light source. Stopping down will help considerably and change the overall character of any flaring that is in the frame. Dropping to 2.8 would have likely eliminated most of what you're seeing in the examples you posted.
As was already said, filters on the lens can cause unwanted ghosting as well (particularly cheap filters).