Pros: Relatively small/light for what it would be in 35mm film equivalent; fast autofocus
Cons: Need to stop down as you approach the 300mm end to boost sharpness; weak OIS
The focal range is really amazing: 200 to 600mm equivalent in 35mm-film terms. That's all in a relatively compact package not that much bigger than the superzoom, and smaller than many ASP-C/DX DSLRs.
Center and Corner Sharpness
Center sharpness is excellent at 100mm, still pretty good through 200mm and at 225mm (I did this to compare with my Tamron 70-300mm VC on a Nikon D5100 at 300mm, because they have equal field of view at those settings), but the Panasonic struggles above 250mm. By 300mm the Panasonic becomes a mixed bag. At f/5.6 it is smeary and contrast is not so good. At f/6.3 it becomes more acceptable, especially with a bit of post-processing. At f/7.1 it's fine and comparable to the Tamron 70-300mm VC or Nikon 70-300mm VR. Basically, the sharpness of this lens wide open goes from great (100mm) to good (225mm) to mediocre-at-best (300mm), but with a little stopping down to f/7.1, you can get that 300mm performance back up to good. Even at f/7.1, though, the 300mm performance corner sharp is a notch below good.
One should keep in mind that this is a 200-600mm equivalent lens, so the fact that it can even take adequate photos at 600mm f/5.6 is cause for celebration. The depth of field is also quite narrow at 600mm f/5.6 if the subject is anywhere near you, so as a practical matter you probably would have shot at 600mm f/6.3 or higher, anyway (unless you were shooting distant mountains or the moon or something).
Autofocus is blazingly fast on my DMC-G3, particularly in single-shot mode. I would put it up there with DSLRs. It's also pretty silent to autofocus, making this lens well suited for taking videos. However, that is in single-shot mode. In continuous tracking mode used against small, fast moving birds nearby, the lens was unable to keep up with seagulls and other birds that I tested against at dusk (dim light). This is not necessary the lens's fault, though, as the camera body makes a big difference as well, and no micro four thirds camera so far uses DSLR-style autofocus (PDAF) which is faster but less accurate. Perhaps with a firmware update and with a camera body with PDAF, this lens would do well even in the very difficult situation of capturing birds in flight in dim light.
Distortions and CA
Distortion and vignetting aren't major problems at all, considering that this is a telephoto and not a wideangle lens. Chromatic aberration and distortion are autocorrected in Panasonic bodies so that they are baked into RAW files. With these autocorrections on, the CA isn't bad at all.
Color Accuracy and Contrast
Color accuracy is bang-on accurate when paired with my G3, and contrast is good when stopped down enough. See above discussion of sharpness.
Optical Image Stabilization
Panasonic's image stabilization is called Mega OIS for this lens. It means when the OIS is on, a lens element will move around to counter your hand shaking. It doesn't do anything to counter subject motion, though, so photographing moving objects at long shutter speeds is still a recipe for subject motion blur.
I've found that Mega OIS doesn't work that well, especially on the long end (300mm) when you need it the most. I have gotten maybe 1 stop advantage, a pittance compared to the 3+ stops I've gotten on other systems' telephoto lenses, such as the Tamron 70-300mm VC on a Nikon D5100. In anything other than broad daylight, I have to crank up the ISO at 300mm, to compensate for shooting at f/7.1 and below. I would prefer a stronger OIS system so as to reduce the need to increase ISO and therefore noise.
The Mega OIS switch is on the lens itself, so you can use it with Olympus cameras if you disable in-body lens stabilization in the Oly body.
Build quality is decent and on par with, say, the Nikon 70-300mm VR. It will take a bit of dinging, but don't drop it from any significant height.
Out of focus blur, a.k.a. bokeh, is okay; you will want to shoot long with large apertures in order to get the best out of focus blurring for ideal subject isolation. I have found the bokeh to be mediocre; not great, not bad. It's certainly enough for casual photos at the bare minimum, and perhaps better than that if you control your composition well.
Focus and zoom smoothness
Focus ring is a tiny little stiff at first, but after a month of breaking it in it is pretty smooth. Still, it's not going to be the smoothest to turn. Zooming action is typical for a consumer telephoto zoom.
Lens size and weight, and balancing with an appropriate camera body
Beware of pairing this lens, which doesn't have a tripod mount/collar, with a smaller micro four thirds camera. It may not feel well balanced, considering the lens weighs 18.3 ounces, which is a few more ounces than a typical midrange micro four thirds camera like the G3. And compared to tiny micro four thirds pancakes like the 14mm f/2.5, the 100-300mm looks like a behemoth, at 5 inches long and 3 inches in diameter. (And note that if you shoot at longer focal lengths, the effective size increases because you're pumping the barrel outwards; so at 300mm, the lens nearly doubles in length. Add the lens hood and it really is a doubling of length!)
On the plus side, the beefy lens makes for easy cupping with your off hand and helps suppress some hand shake from that source.
Lens hood, pouch, and filter size
Comes with lens hood/pouch and uses the relatively common and inexpensive 67mm filter size. The lens hood is of good quality and won't rock back and forth much.
The bottom line:
This lens is a bit of a mixed bag. Ignoring non-MFT lenses (which do not have autofocus since you have to use an adapter), these are your choices for medium to long telephotos:
The Panasonic 45-200mm is not as sharp as the 100-300mm, at 200mm. So if you want sharper performance and don't mind the extra cost and size/weight, get the 100-300mm.
The Panasonic 45-175mm X has some teething problems with OIS right now but is a great alternative to the other Panasonic zooms, if you do not need anything longer than 175mm. It's also relatively small and light due to its power zoom (press and hold to zoom in/out, rather than using your hand to manually twist), which allows for smoother zooming for videos.
If you do not need optical stabilization but still want autofocus, the Olympus lenses are options:
The 40-150mm is a pretty good lens, very sharp at 40mm and still pretty good at 150mm. Very small and light for a telephoto. But it tops out at 150mm. Lack of OIS is not a problem if I'm shooting moving things, anyway, like birds.
The Olympus 75-300mm is not a good value. It's smaller than the Panasonic 100-300mm, but lacks OIS, and isn't quite as good optically, and costs much more.
There are also Panasonic and Olympus superzooms, like the Panasonic 14-140mm, but those fare even worse in sharpness at long focal lengths than the Panasonic 45-200mm, so they can not seriously rival the 100-300mm at 140mm, let alone more than 150mm (because they don't even go past 140 or 150mm in the first place).
Then we have the Panasonic 100-300mm. It's the largest and heaviest, but only compared to other Micro Four Thirds lenses; it's still pretty compact compared to similar DX/APS-C DSLR lenses. It goes to a crazy focal length and the OIS is good for a stop of stabilization, though it does require stopping down to at least f/6.3 to get adequately sharp JPEGs; you may be able to finesse f/5.6 shots with enough Photoshopping, but that's not a fun situation to be in. Since it requires a bit of stopping down and is equal to 600mm on a 35-mm film camera, and the OIS is weak, you are looking at about 1/500 second exposure times to get something reasonably sharp, 1/250 second if your are lucky. (And that's against a stationary object, with proper technique including cupping the lens with one hand and placing the camera to your eye to act as another point of support, with proper stance. Using a long telephoto lens well requires practice.) This means shooting in broad daylight if you want to keep ISO at 400 or below. In dim light, to get 1/600 second exposure time, you will need much higher ISO which destroys image quality with noise.
If you're okay with the 100-300mm's limitations, size/weight, and cost, there is no better medium-to-long telephoto lens in the Micro Four Thirds lineup today. If you can give up some reach, consider the Panasonic 45-175mm or the Oly 40-150mm as cheaper, lighter, smaller options, though you do give up in-lens stabilization for the Oly 40-150mm.