Sounds like you have already covered all the bases.
The typical problem is motion blur caused by camera movement due to poor hand-holding technique. As the sensor resolution increases, the camera points out your flaws out to you more easily. For example, what might have been a two-pixel blur with your D300 now may be a seven-pixel blur with the D800.
To combat this, you can either use a support like a tripod or wall, turn on the VR if the lens has it, or increase the shutter speed to freeze the motion. When folks do the higher shutter speed, the question becomes how fast is fast enough? The answer to that question depends on how steady your hands are to begin with.
The old film SLR rule of thumb was 1/L, L being the focal length of the lens. The DX bodies with the crop factor tended to suggest a 1/(1.5 x L) starting point. For the D800 and similarly dense sensors, 1/2L is not out of the question depending on your hands.
Once you figure out what you need for speeds, you can then play in the gray area using VR. Depending on how shaky your hands are, you may not get all the stops of support the marketing dept. claims.
Back in the day I could hand-hold a 200mm at 1/15 with no trouble. Not any more....
---------+---------+---------+---------+---------+ Joseph K Seattle, WA, USA