Ultra wide-angle lenses (fisheye) give you a view that is wider than your eyes. They permit showing panoramas, without the need to pan (and you all know how bad that is with RS...). They also permit interior shots where you have little room to stand back. And they create interesting distortions for subjects up close.
Such lenses have almost infinite dof, so low-resolution cameras cannot hide behind a lot of defocused area. A wide panorama that has low resolution really looks bad.
With 4K, one can really exploit uwa lenses. And that is what the Panasonic A500 has - a fisheye lens and 4K. You can also put a fisheye lens on a GH4 and get the same effects (at considerably more cost).
Here are two 4K videos that make use of the fisheye, for its panoramas and interesting distortions. The first is shot at the East River in NYC (boats, ships, helicopters, strollers).
Here is an illustrative frame grab:
The second was shot at various parks in NYC. It has also has a few low-lit interior shots (at McDonalds, Starbucks, underground subway station). Both videos as a bonus have a time-lapse sequence as well.
The second video:
Illustrative frame grabs: