About the subject of the thread, the obvious camera shake, the P1000 can reach up to 3000mm focal length (full frame equivalent). The rule of thumb is that you can handheld 1/focal length (full frame equivalent) sec shutter speeds. So in order to handheld 3000mm without image stabilization you'd need a 1/3000 sec shutter speed. Thats almost the maximum shutter speed available (which is 1/4000 sec) and needs most excellent lighting conditions if the shot should be taken at base ISO.
So yes, this image clearly suffers from shake, but I dont think turning off image stabilization will be an easy solution, at least not if you're below 1/3000 sec shutter speed at the far end of the zoom range.
About the image quality, the P1000, being an extreme superzoom compact with a tiny sensor, is not able to actually archieve really high image quality, even under the best conditions.
Dont get me wrong - its absolutely amazing and mindboggling how much image quality Nikon actually managed given the conditions, and Nikon has proven their skill in both lens design as well as post processing to offer this level of image quality. They are clearly ahead of superzoom compacts from most other companies (except Fujifilm). Still in absolute terms the image quality archieved even under the best conditions is pretty mediocre, thanks to the very small sensor (1/2.3 inch, or 6.17x4.55mm) and its incredibly tiny pixels. Very likely the actual resolution would raise if they could make the pixels larger, unfortunately people blindly believe what you write on the camera, so 16 Megapixel it had to be, since thats kind of the lowest value people would accept at all.
Personally I'd had simply use the Sigma Foveon trickery and used a 3cmos construction, as it is known from some video cameras. Meaning the three colors R, G, B are split with color dependent mirrors and reflected on three separate sensors, one for each color.
Such 3cmos constructions need to be very precise and thus cant support too high resolution. However because one measures three color values in every pixel instead of just one, its actual resolution, not the usual propaganda. While the output of regular sensors with a color filter array only records one color per pixel and has to be post processed with what is called demosaicing, which tries to guess the missing color information. This process loses about half the official resolution, which is why the Megapixels specified on pretty much all current cameras are total propaganda.
Thus what can be done is using for example three 10.5 Megapixel sensors and already reach an effective resolution thats higher that you get from a 16 Megapixel sensor crippled in resolution by a color filter array. AND these pixels are larger and better. In fact the total pixel size you have available is now like five times the area from before, though this size has to be split between three different color channels.
Such a construction would be pretty expensive, due to the precision required - but this camera is already pretty expensive anyway, thanks to the large optics required for the extreme zoom range, even for a tiny sensor. I thus hope the extra expense wouldnt be such a problem.
Also, importantly, you can use the aforementioned Sigma Foveon trickery. That measn you can now legally write "31.5 Megapixel" on the camera. Because thats what Sigma does with their Foveon sensers, they add the pixels from the individual color channel, so a 15 Megapixel sensor turns 45 Megapixel etc.
It should be noted that Foveon sensors work very differently than having a 3cmos construction using color dependent mirrors. The Foveon technology actually lose a lot of light in their process and have frankly pretty mediocre performance, especially a lot of noise in the red color channel. Which is why using Foveon instead of regular sensors wouldnt solve any problem at all, even if Nikon had access to the technology (its patented).
A more realistic estimate for the resolution of a Foveon or 3cmos sensor with 10.5 Megapixels would be about 18-20 Megapixels. This varies a lot with the image in question. Especially an image thats predominantly red or predominantly blue will not archieve much resolution with a Bayer sensor at all, because only a quarter of the pixels record red and another quarter record blue.
However thanks to 3cmos these pixels are now much larger, of higher quality, than the 16 megapixel bayer color filter array sensor used before. And the demands to the lens have also been lowered, because the pixels are substantly larger now. This is especially important because the extreme lens is of course diffraction limited even wide open, which is f/8 at 3000mm, so the larger pixels directly result in more resolution anyway.
In the sum the effective resolution as well as the image quality would have been raised compared to the current solution.