I did try cleaning the contacts with some DeOxit contact cleaner (not sprayed near the lens, of course!). Unfortunately, it made no difference. I'll give the Isopropyl alcohol a try. I suspect the problem may be internal to the lens, since the issue only occurs when the lens is zoomed in nearly all the way.
Alan, I had the same suspicions about the 24-120's sharpness when I moved up to the D800. Would the lens hold up to 36 megapixel scrutiny? I was actually pleasantly surprised... It is remarkably sharp in most situations... even wide open.
I'm still planning to upgrade to the 24-70 2.8 and the 70-200 2.8 VRII soon... but I'll keep the old 24-120 for less formal shooting occasions when I don't want to carry a lot of hardware around. May have to send it to Nikon for repair, though, if I cleaning the contacts doesn't solve the focus problem.