It's possible the body register is off but far less likely than the lens or finder calibration. In order for the lens register to be the issue, the only likely explanation would have to be the camera had some impact damage or a person tampered with the adjustment. Unless a camera's had a major hit, this is not something that tends to go wrong—meaning there's little reason someone would be inclined to mess with it (unless, of course, disassembly was needed to repair something else and the re-assembly resulted in some misplaced or absent shims perhaps, but I'd suggest the odds of this are also rather long).
Still—do not lose sight of the big picture. Presently the F has an issue somewhere, you're aware of that—but it can't be remedied, until it has been located.
If you have some other lenses and or bodies, much time might potentially be saved via some quick substitution. You've not mentioned access to additional lenses or Nikon bodies so I don't know if this is feasible for you.
But Eg if the 50mm lens in question hits infinity at its stop on another, known-good body, you can be reasonably confident the lens is not at fault, and concentrate on the test camera, first.
On the other hand, if the 50mm lens behaves exactly the same way fitted to another, trusted, body, I would be inclined to, obviously, investigate that, first.
Let's assume the lens itself happens to be OK. To pinpoint the root of the problem the correct place to start is at the film plane. You could think of this as the master, or primary calibration. In virtually any design of camera that facilitates focusing verification by the user (as distinct from scale focus) the camera body is adjusted either to achieve best possible focus between body and lens (if a non-interchangeable lens design), or to a standard lens flange to film plane dimension (interchangeable lens design). The viewing system for adjusting the focus is then dialled in to match the film plane—never vice-versa.This is actually the case whether the design in question happens to be a single lens reflex, twin lens reflex or even a rangefinder. The schematics may differ but the principle is the same.
When, and only when, it's been verified that the body calibration (or body to lens, in the case of a fixed lens design) is good, should adjustment of the viewing system be attempted.
The F is obviously an interchangeable lens camera. There are various ways to measure the lens register. Vernier calipers, whilst not as accurate as a high quality depth gauge and surface plate will still get you close enough to get started, providing you can ease their jaws across to both the relevant surfaces. Given you must take a measurement off the inner rails and not those for the pressure plate, (or have the jaws fouled by any other part of the body), this may or may not be quick, easy and repeatable.
If using a depth gauge and surface plate parallel blocks or another object with accurately parallel planes will usually be needed to get the critical measurement off those film rails instead of, say, the rear of the body which will be incorrect.
I have carried out these inspection procedures on a number of occasions, and still do from time to time, if I think it's necessary. Depending on what other equipment I have on hand though, I'll exercise quicker options if they're appropriate.
Eg as mentioned above, if I have access to other lenses and bodies that are known to be in good adjustment, checking the focus image of those lenses at the film plane of the test camera, and that of the test lens at the film plane of another, known good body, will quickly and accurately eliminate the various possible locations of a focus problem.
Assuming you don't have any other lenses or bodies in your shoes I would probably start by inspecting the focus of the lens at the film plane. A ground glass and loupe, or a trusted SLR may be used to do this.
If you can verify that the film plane image actually agrees with the finder image at all focus settings—whilst this does not, in itself, verify that the relevant lens register of the body is good—the balance of probabilities is such that you may proceed on the assumption that it's OK, because film plane and finder images being a good match—the lens, if it's going substantially beyond infinity at the film plane, will almost certainly out of calibration.
On the other hand, should the film plane image show a sharp infinity image with the lens at its infinity stop, then, from your description above—the focus screen//eyepiece diopter/mirror condition are suspect, and require investigation because there is an unacceptable divergence from the film plane.
Cheers,
Brett
