Many Nikon D600 owners are complaining of usual dust and or oil specs appearing on their sensor. had 20 D600 bodies and reported that all 20 of them developed this issue within the first 3000 shots and none after.

Nikon also recommends turning the camera upside down and blowing the sensor off with a blow bulb, and I can tell you right now, that is about the worst way to clean your sensor. (Simply because many of those bulbs are full of junk and lint and you run the risk of making it worse). My advice would be to shoot your 3000 shots, and get it professionally cleaned (by Nikon) if you are uncomfortable doing so yourself. The D600 is a terrific camera, so dont let a little issue like this stand in the way of enjoying it.

Nikon Support on D600 Dust/Oil Issue