I had focus issues with an early production run of the 3+ Black, which resulted in an uneven focus, especially in the bottom left of the frame, but it was a bit more pronounced than what your video is showing. GoPro replaced the camera free of charge under warranty, and the difference between the two was extreme.
Check the serial number inside the battery compartment. If it has 0813, 0913, 1013, 1113, it most likely has the production focus issues, and you should be able to return it for a newer one, assuming it's still under warranty (the digits will be split between the two lines, with the final "3" being the first digit on the second line).
If you're not still under warranty, you can try the manual fix outlined here, although it's probably not for the squeamish:
[youtube]https://www.youtube.com/watch?v=SnLdpSRMsEs[/youtube]
As for the washed out look, it looks like you're getting a lot of flare from the sun, but it's kind of hard to tell. Are you using any filters or other protective lens covers? It doesn't seem quite as bad when you're pointed away from the sun. Do you get the same issues when flying around the middle of the day, with the sun more overhead?
You can also try turning on spot metering to get it to set brightness levels based on the center of the frame as opposed to a more generalized average. If you have a bright sky in the background, it will average the overall brightness to fit that, and any darker foreground will get muddy. Off the top of my head, I don't remember if spot metering is a ProTune-only setting, but dig around and I'm sure you'll find it.
And have you updated to the latest firmware? It offers a few additional settings to help control the exposure, including max ISO and a manual exposure override, but again, I'm not sure if these are ProTune exclusive settings.
Hope this helps.
Thanks,
Cary