I spent last weekend with the GH4 shooting footage in Appanoose County, Iowa thanks to director Nick Young of Cairn Productions. The shoot gave me plenty of opportunity to learn more about how the Gh4 performs. In short, it was a joy to work with, and I couldn't be more pleased with the images I'm getting. Take a look:
I've had the camera for a little over a month, and I'm finally closing in on my preferred Picture Profile and settings. Here they are:
Picture Profile: Cinelike-D
Contrast: -1
Sharpness: -5
NR: -5
Saturation: -1
Hue: 0
Highlights: -3
Shadows: 0
Master Pedestal: 0 (set to -1 to -3 when using vintage lenses or in heavy backlight which lifts the blacks)
Luminance Level: 0-255

Cinelike D is impressing me more than I thought. Back in the days of the DVX100, one needed to be very careful shooting Cinelike-D, as blown highlights looked particularly heinous. Also, Cinelike-D's flat response required adding an S-curve to give it more contrast, but back in the days of 8-bit color correction, this could create ugly banding in gradients like skies.
With the GH4's resolution and dynamic range, and with modern 32-bit color correction, blown highlights and banding are no longer a problem. Of course, careful attention must be paid to exposure (this is not a RAW camera after all), but highlights roll off pretty well, and I have yet to see any banding artifacts when I grade the Cinelike-D image in Premiere Pro. If the footage looks this good when it's 8-bit 4:2:0 h.264 files, I can't wait for 10-bit 4:2:2 Prores files when the Atomos Shogun becomes available!
I've also discovered that there are situations where Cinelike-D creates good imagery without the need to grade in post. Sunsets, magic hour and shots with lots of black in the frame look great in Cinelike-D straight out of the camera. In the video above, the shots of the fisherman at sunset have no contrast added in post. I only adjusted exposure here and there and boosted saturation on the wide shots. Other than that, it is untouched.

A Note on FilmConvert for color correction
I did not use FilmConvert to grade the above video. I tried but was unhappy with the results. Often, FilmConvert makes footage look more cinematic, but there are certain types of footage where it just makes the image look much worse. I have found that shooting sunsets and shooting green foliage does not benefit from FilmConvert's mojo, no matter what Source Camera or Film Stock I choose in the interface. Green foliage tends to turn brown, and I'm quite certain I've seen nice greens in films shot on Kodak and Fuji film. FilmConvert also does strange things in the highlights of sunset shots, creating unrealistic divisions between colors rather than smooth gradients. Some settings work better than others, but it is easier to get good results just using curves and the color corrector in Premiere.
Color Grading in Premiere Pro

The above video was graded in Premiere Pro. This mainly consisted of adding an S-curve using RGB Curves. I used the Fast Color Corrector to adjust saturation as needed. I find it's saturation slider more useful than the Three-Way Color Corrector, which works differently and less intuitively.
Last, I created an Adjustment Layer above the clips and to that I added the Lumetri "Cinematic 2" look. That way I could adjust the strength of the effect by lowering the opacity of the layer on a shot-by-shot basis.

Final Thoughts

I am extremely happy with the sharpness and color tonality of the GH4. It is very easy to use. The added features like focus-peaking and zebras allow me to get good imagery much more easily than with the GH3. For the entire weekend, I didn't use my external monitor at all. I was able to use the LVF and the LCD to check everything. Oh…I almost forgot! The WiFi works on the GH4 too! The director used the Panasonic Image App on his iPad to check framing, etc. while I operated the camera. It worked really well. The only real problem is that, once you are recording, you cannot adjust aperture, shutter or any other settings on the camera itself as it's expecting to be controlled remotely by the app.
In any case, I am falling in love with the GH4.