Having recently moved up to a full frame sensor (D610) I was under the impression that the oil on the sensor issue has been resolved. But after returning from my holidays I've noticed on some of my photos had spots on them (See attachment in the sky portion of the photo). After reading some forums is this something that will go away in time and prevalent in new cameras or has Nikon not fully addressed the issue with the D610. Another question would be to have the sensor cleaned by a qualified repair facility (mine is still under warranty) but after the warranty expires what are the risks on having to clean the sensor myself.
Some dust, and even occasional oil splatter, is common. The tip off with the D600 was a huge amount of oil splatter in what looked like the upper left of the picture, that would return fairly rapidly after a cleaning. In this case, I'm having trouble seeing what you are posting (bad monitor at the moment), but you might want to try a blower and then test again to see if the spots have moved.
It's not easy to tell at that size, but given that the shot was at f/16 these could just be "normal" dust rather than oil/debris - which from all we have read is indeed fixed with the D610. FX cameras do seem to show a little more dust that DX, so this is almost to be expected.
A quick look through older posts will reveal many threads covering sensor cleaning
Clearly you have at least a dozen dust spots in the cloudy sky portion of your nice low-tide shot. Given that you shoot at small apertures with interesting foreground objects and at slow shutter speeds in a beach environment you will need to clean your d610 sensor frequently. Since your blower does not remove the dust, try using an electrostatic arctic butterfly brush and/or a wet cleaning with visible dust or eclipse solution applied to visible dust ultra mxd swabs. Others on this forum are advocates of gel-stick devices. You should also acquire an illuminated magnifying loupe to help you identify where on your d610 sensor the dust is located. Good luck.
It looks like normal dust to me. Keep in mind the FX sensor is more than twice the size of the DX sensor - so there is twice as much room to collect dust. Oil is unlikely - there is a lot of surface area inside the mirror box and dust normally accumulates in a lot of places. You clean the sensor, but also need to use a blower on the entire mirror box area.