Still deep in play mode with my D600, but, as Eric points out, there is a setting under Auto WB for preserving warm feel from indoor lighting, which I have been experimenting with this weekend, along with playing with ISO in all variations of lighting and lack of lighting - I'm not used to being able to shoot in such low light and to get such good results. I haven't seen the green shift, but my color perceptions are a bit skewed sometimes.
I don't think KR's review is bad either - I was just poking fun in another thread. While still too early to tell, his declared love for the D600 as being the right combination of technologies for those considering the move to FX, seems to be a sound observation.
But, so much more experimenting and playing to do to really see what this D600 can do . . . .