I looked at a similar deal online and was very tempted. I passed, because the price will only go down and I wanted to give Nikon some time to work out a couple of issues (dust and oil on sensor and such). If it were me, I'd plan on sending the D600 in for a cleaning and checkup in a few months, after letting it all shake out. Nothing new about this, the D7000s had the exact same issues right off and all was well.
It's funny because I bought my D7000 when everyone was all up and arms about focus issues and oil on the sensor, but I manged over 6000 shots with zero dust/oil issues with photos. I almost didn't buy it because of all the posts but I'm glad I took a chance. From what I understand Nikon did nothing to the camera post release other than firmware updates, so either the hysteria was for nothing or the actual percentage of shipped cameras with issues was so low it sorted itself out.
There are always a small percentage of cameras that have issues but after my experience with the D7K I'm confortable with taking a chance because while I'm not saying I won't have problems, I'm also not going to chase white screens at f/22 just to sleep well. Also, the vast majority of reviewers hammered out hundreds of shots and had no problems with oil/dust. There were a few that had issues, and only a couple that I saw where serious enough to consider the camera defective. I'll consider your advice about the checkup though.
The problem with forums these days (esp dpreview.com), is that if one person creates a post about a problem, 10-20 people repeat it in other posts. Eventually you have a rabid community who believe that there is some huge issue which very well could be isolated to a small group of cameras or specific scenerios. It's almost funny because many of the people who repeat it often don't even own the hardware they are criticizing. Anyways, I'm not trying to downplay any issues the D600 might have. I'm just not really worried about it for now. Besides, for $700 in savings it was worth the gamble!