Nikon exchanged my D600 for a D610 which arrived on Monday, since then I've had 3 lenses on, one of which was on for 3 days to shoot macro. In that time, I've watched the dirt build up on the left hand side of the sensor just the same as it did with the D600. General dust would be all over the sensor, this is most definitely limited to the left side exactly like the D600. I'm now waiting for Nikon to get back to me with what they intend to do about it, but it's most certainly a problem and something I wasn't expecting at all.
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What aperture did you use when you took this photo? Anything smaller than f/16 will show every spec of dust. Most cameras will have some spots, but if you are shooting macro with really small apertures, be prepared to see some spots.
Make sure when you change lenses to blow off the rear element of every lens first. You might have dirt there that is transferring to the inside of the body. Did you try using a rocket blower to blow the inside of the body to see if it would remove any of these spots?