Given that I personally had one warranty repair come back and immediately have the issue again, and I personally know someone here who is about to send theirs back for a 3rd time, while others have had hardly a spec of evidence of the problem (pun slightly intended), one would have to assume that this is a sporadic problem that they just have not been able to wrap their arms around. So, it would seem that any D600 manufactured at any point may or may not exhibit the issue. It's an absolute crapshoot as to whether one out of the box will have the issue.
If I needed to summarize the problem, whoever is manufacturing the shutter cannot do so consistently at the required quality levels, and there's no fixing the problem. Given the upgraded frame rate on the D610 one has to assume you're getting a D600 with a completely revised shutter assembly and not much more (other than white balance software tweaks).