The big advantage with the is that they are relatively cheap, and, not least, very compact. The lens here is surprisingly short for a 300mm tele lens.
On the other hand, there are drawbacks, for example, manual focus only, fixed aperture, no zoom, and loss of contrast when you have a bright background. Read more about this in my review.
Another drawback is the lack of image stabilization, which makes it near impossible to use the lens without a tripod. Even focusing correctly or framing is hard without a tripod. And this is where a newer camera like the Lumix G85 comes handy: It has built in In-Body Image Stabilization (IBIS) which makes this lens much more usable. See the sensor movement demonstrated here.
Notice that the lens above has electrical contacts, which is unusual for a manual focus lens without any aperture mechanism or image stabilization. However, it is still useful because it tells the camera the right focal length, so that you don't need to input it manually for the IBIS to work well.
Also, it signals to the camera when you operate the manual focus, so that it can show you a magnified view, if you have setup the camera to show this.
To illustrate how much easier it is to use on the Lumix G85, compared with the Lumix GH4, which does not have IBIS, consider this comparison video:
As you see, with the Lumix GH4, which lacks IBIS, it is impossible to focus or frame the lens, even if I support the camera and lens with both hands, and support both elbows on a windowsill. With the Lumix G85, though, the lens becomes usable, even without a tripod.
Note that Olympus cameras can also stabilize this lens. However, due to the way Olympus cameras operate, they only stabilize the viewfinder while you half press the shutter button. And half pressing the shutter removes the magnified view. So with Olympus, you can only get the focus aid stabilized for a split second at a time, which is quite frustrating. Not so with Lumix G85: Using the lens becomes fun!
Here is an example image taken handheld at 1/25s, f/6.3, ISO 3200:
Note that the focus is not perfect here, and there is some blur. But keep in mind that 1/25s is way below safe handholding speed for a 300mm lens, in fact, it is five stops below. You'll notice the typical out of focus donuts in the background, due to the mirror design of the lens.
If you just want an inexpensive, very long lens, then get the Lumix G 100-300mm f/4-5.6. It is a good lens at a good price, and will give you much better pictures than the mirror lens. The mirror lens is more of a fun novelty item, in my opinion.
In the picture below, you can see the Lumix G 100-300mm at 300mm (left), compared with the Tokina 300mm f/6.3 (right):
The picture clearly shows the size advantage of the catadioptric mirror design of the Tokina lens, making it remarkably short.