In reply to jethro kiernan:
1) Did you try AF fine tune with each and every one of your lenses (not just the 50mm)? It's lens specific, after all. I think the newer Nikons can even automate the process (although the 810 probably not). Get a good lighting, large enough AF target perpendicular to the camera and a ruler at 45degrees next to it (or one of those pre-made AF calibration targets). Distance matters as well.
2) The AF (not in live view) always focuses wide open - thus if your primes are faster than the zooms, any misalignment will be more pronounced with them (even if you shoot them stopped down)
3) What CH wrote, check the AF fine tune settings with every lens, there might have been settings set by a previous owner for their lenses messing you up.
4) Remember, you have two variables that need to match - the lens and the camera (used to be just the camera, but nowadays the lenses are so full of electronics, distance sensors etc that it matters). If your camera is say -5 from correct (meaningless units, just as an example), your zooms +5 and your primes -1, the zooms will seem to be ok even when they are actually much more out of alignment than the primes... Especially if the primes are faster, even one stop can make a big difference.
You could finally let Nikon check at least the body with their reference lens or an optical bench or whatever they use (at best with all your lenses), but that could be pretty long and costly wait unless you are a member of NPS.
Post edited at 12:49