I may have missed this if it has been posed before. I bought a D600 almost a year ago and it was a refurb. I haven't had any serious dust problems but was wondering how to tell if the shutter has been replaced?.
You can set the camera in the mirror up mode and examine the screws on the top of the shutter unit very carefully. If there is any evidence of change, you should be able to tell by any evidences on the screws. Or simply send it to Nikon so that they can change it for you. By the way, refurb D600 body is priced as low as $1215 as of yesterday on Nikon's web site.
They marked my camera with a black dot inside the tripod mount. Mine was not a refurb, but I'm sure they would have done the same if they had serviced your body. From what I've heard, that is how they've been marking the cameras with new shutters.
Paul
FWIW -- I was also not having any issues with oil spots, but I sent it in anyway just to be done with it.
I bought one from the B&S board and sent it in after three weeks. I got it back in two days and Nikon says it replaced the shutter, but the shutter count is about 1000 more than my last count.
The funny thing is now the LCD starts to have the greenish tint that wasn't there before. No biggie, just dialed down to M1 in WB, which affects JPG too.