While the Nikon F SLR mount hasn't changed since 1959, the ability to mount the lens on the body doesn't necessarily mean that all lenses maintain all functionality on all bodies, even if they have compatible mounts.
The F4 era camera bodies were the first generation of autofocus and program exposure bodies that were made by Nikon. The tricky marketing problem Nikon faced at this time, in the late 1980's was maintaining compatibility with the older MF lenses that most users owned from the manual focus era. The Nikon F4 maintained remarkable compatibility with most of these lenses, but as time progressed, the lenses were updated and full compatibility with the newest lenses is no longer feasible with the F4.
The newest Nikkors that own are AFS "G" lenses and some have vibration reduction (VR). The biggest issue with the "G" lenses is that they do not have aperture rings that were required by the F4 to control the lens iris in the exposure modes most often used by advanced users. The loss of manual and aperture priority exposure modes is a big loss while using the F4. In addition, the VR feature is not supported by the F4 as it does not have the multiple AF sensors that are required to use this feature. This is not a huge loss in compatibility compared to the exposure modes, but still frustrates the user of a high-end lens to have a key feature disabled on a longer lens.
While most users are aware of the aforementioned limitations of the "G" lenses on the F4, it took some experimentation with my AF-S 200 f2G VR and F4s to find some other quirks in the lens/body combination.
The first thing that I discovered is that the DOF preview lever does not work properly. On later model bodies, the DOF is an electronic operation, but on the F4 is is still a mechanical operation where the button operates a cam that moves the iris control lever. With the "G" lens, it moves the lever to the f22 position and will not depress to the camera-selected aperture.
The second issue that I found concerns the selection of the buttons on the front of the lens. The function of these buttons can be selected to perform one of three tasks with modern bodies: 1) AF-lock, 2) memory recall, and 3) AF-on. The first two functions work quite well. The AF memory can be set and the focus point recalled in an instant with the AFS motor. AF lock also works quite well, but the AF-on button not only fails to function, but will totally disable the AF system in the camera. So if your AF doesn't work when you mount this lens, check that you aren't selected to "AF-on" on the lens itself and see if that doesn't fix the problem.
While the new "G" lenses aren't the greatest thing to try and use on the F4, you still have the option if you move to the correct exposure mode and don't mind loosing the VR (if the lens offers it as an option).