Not sure it's post-processing. I've just picked up my third copy of this lens, it's just such a good all round long lens, and am looking forward to using it again.
Based on my experience of the first two you need to be a bit of a Zen master to make best use of it. In any sharp shot the focus accuracy has been critical. You can tell a shot where critical focus hasn't been achieved and where PP has been used to try and rescue. With the 150-500 you need to be aware of shake, sharpness of the image in the view-finder and the OS. When you let the OS settle and pay attention to the image in the view-finder and take care with your shutter press then you're likely to get a critically sharp shot. if all 'ducks aren't in a row' here then the image will likely be a tad out of focus and you get the very slightly soft, smeared detail that is apparent in many shots in this thread.
The other thing to remember is that the lens tends to perform best stopped down to f8.0. You need to experiment a little as some copies will perform better than others, same with most zooms. Some will do well at 500mm and some will be better at 450mm or so.
So, you need to hand-hold in a steady, relaxed manner, watch your breathing, watch the image sharpness in the viewfinder, pay attention to the OS and stop down and avoid, in some cases, 500mm.
With modern DSLR bodies you can up the ISO to get decent shutter speeds ... and depending on the body then noise shouldn't be too much of an issue. Again, you need to practice. Listen to the shutter and if it sounds too slow then change ISO rather than open up the aperture.
In terms of image quality this lens will never compete with the likes of the 400mm 4.0 L, 300mm 2.8 VR, 200-400mm 4.0 VR and so on, but get everything right you'll get some superb images and maybe you'll even achieve enlightenment 
