Do you trust your focus on the D600?
Had the issue with my D7000 that uses the same AF configuration. I was trying to understand if it was my technique.
Never had the issue with D100,200,300, D2x, D800
I often found that the camera would focus on something totally different to the AF sensor that I was using. I was always careful to select a contrasty part of the image in order that it would lock on.
The frustrating thing was that when it did focus it was spot on. Just not very consistent.
Might be an idea to share how you have the AF setup.