Lensrentals noticed that all of their D600 rental units needed sensor cleaning after being used. What is even more interesting is that all spots seems to be located around the same area - the upper left portion of the sensor:
Lensrentals did some additional investigation and found that "D600′s shutter curtain opening seems a bit larger than the other Nikon cameras with a bit of a gap around the shutter curtain. It may well be the shutter movement is pulling dust onto the sensor":
Similar dust/oil spots have been widely reported on Amazon's customer reviews, on [NR] Forum and other websites. As of today, there is no official statement from Nikon and I don't think there will ever be one.
Just a reminder that many of the first D800 cameras also had an unusually high amount of oil/dust spots on the sensor. It seems that this issue was resolved with later shipments.