Thanks for your comments. At least I know I'm not alone in this. I understand from Scott that batteries are not covered by Nikon. This may be true but how did they handle the problem with the EN-EL3 several years ago? Wasn't there some problem?
But all this seems to focus on what the battery is "telling" the D800. I wonder if there is a problem in the way the *camera* is processing the information from the battery. This would be a defect in the camera, not the battery. Perhaps some Nikonian who has two D800's or some other camera which uses the EN-EL15 could check to see of the same battery reading is given by both cameras. Wouldn't that tell where the fault lies?