These are the "hot rods" of the Nikon F world, special models that were either one-offed by Nikon or modified by the user.
My original text, based on rumor:
This is perhaps the best known of the special models. These have a red dot next to
the serial number and reputedly don't lose a frame when working the mirror lock-up on the camera. Not having
any personal experience with a Red Dot, I'm not sure exactly how it works. Del's
Camera mentions (in their September 1996 flyer) a F Mirror Up Button camera, which
might be either a Red Dot or a special factory modification. There are rumors circulating
over the usenet that the red dot was placed on the top plate when it was sent back
to Nikon for repair that involved replacing the top plate, to indicate that the given
serial number was not the original one. By the way, Pacific Rim Camera indicates
that all 66xxxxx models are red dot models (and are all fairly rare).
Sources: see my bibliography page. I mostly consulted B. Moose Peterson's book for this one. I also owe a deep debt to the online version of the Gray's of Westminster letter for much intelligence regarding the KS-80A and the F-H. Hayao Tanabe set me straight regarding both the Red Dot and the Early versions of the F, and provided priceless knowledge about the Model I, II, and III meters. Ted Wengelaar provided serial number and existence information regarding the White Leather F's.