Nikon has finally stepped up to the plate and offered to service Nikon D600 units that have spots that can't be removed by a blower.
Here is the announcement: http://support.nikonusa.com/app/answers/detail/a_id/18180
Nikon USA Quote: "Some D600 users have reported the appearance of random spots on their images which is generally attributed to the natural accumulation of dust. While understanding that dust will occur over time, and steps may be taken to reduce the occurrence, the complete elimination of these dust spots may sometimes be difficult." (underline added)
Note that Nikon only mentioned dust spots. Nothing about oil. So far I agree -- I still haven't seen solid evidence of oil spots.
Nikon claims that the spots are from 'natural accumulation' of dust. They do not admit that the D600 has an unusual susceptibility to dust, or that the dust may be internally generated by the camera. Interestingly, Nikon Europe has a very differently worded explanation here.
Nikon Europe quote: "Some users have indicated the appearance of multiple granular dust spots in images captured with the Nikon D600 digital-SLR camera. These granular dust spots are reflections of internal dust generated with camera operation, or external dust particles that have found their way into the camera, either, or both of which, have adhered to the camera's low-pass filter." (underline added)
Nikon Europe's explanation appears to vaguely allude to internally-generated dust from the D600.
Both Nikon USA and Nikon Europe recommend that you first use the built-in sensor cleaning function. If that doesn't work, use a blower (DO NOT make contact with the sensor with the blower or with a sensor swab). If that doesn't work, call them for service. Makes you glad you bought a Nikon domestically and not gray market.
See Nikon D600 Resource Page (under "Dust/Oil Spots")
Firefly DSC-2000 Review