@hark: "too dark to be oil" ???? too green to be a leave??? too white tto be milk ???
"Plus there is an odd size elongated spot near the top--oil tends to be rounder" : this spot is just a place where three spots come together... But what you want to say is: ok 500 spots but a few of them are not oil but the 490 others are oil ???
Those darker spots do not look like the oil spots I had on my D600; therefore, I surmise the debris stems from something else besides a faulty shutter. As someone (maybe Dave_W) mentioned, some of us take precautions with where we store the body and lens caps rather than dropping them freely in the bag or placing them in a pocket. Any dirt or dust will easily transfer from the caps to the inside of the camera's body.
@sonicbuffalo: Dust ok, hundred of spots: not OK, the spots are the same as on my D600 (witch was replaced by a D610 by Nikon). Never had a similar problem with a D90 or D700...
Okay...this tells us that you've been through the process once before where you sent in your D600 directly to Nikon. So WHY are you asking for our opinion? If I was under the impression that my D610 had the same issue as my D600, I'd FIRST upload a photo to Nikon's site so one of their techs could take a look THEN possibly ask for the opinion of other esteemed members here. Obviously we aren't telling you what you want to hear. The bottom line is it does NOT look like an oil shutter problem to me. But rather than take my opinion or the opinion of others, you SHOULD ask Nikon for their opinion.
Please don't be surprised if they tell you it looks like dirt/dust. If Nikon determines it is dust/dirt, then I don't think they would cover it as a warranty repair.