So I just bought a new D600 this weekend and discovered dozens of "spots" all over the sensor. I did some Googling and learned this is happening to quite a lot of the new D600s and older D7000s as well. Apparently there is oil/grease that is being thrown on the sensor when the shutter is activated. Many people are just cleaning the sensor only to have the grease spots return.
I thought about cleaning it on my own. However, after spending $2100 and fear of voiding the warranty, I don't feel it's a good idea. This is disappointing and I am just going to return the camera.