No. That only affected 25% of them and Nikon genrously replaces 100% of the shutter units, not questions asked. So if you come after 100k shots, you still get a new shutter unit... that alone makes the D600 the best used deal ever.
Friend of mine had hers replaced with a new D600 which had the same issue; then she returned that one and got a D610. She saw my D810 and sold off the D610 and is much happier with the D810.
I used the D600 and D800E in parallel for one week of heavy shooting when they came out in 2012
Result: The D800E was better in in the field, better AF, more consitent white balance, the D600 was better in the studio as Digiback on my Sinar P2 monorail, had a much better tonality and only slightly less spatial resolution. The D600 was for my usage simply the better camera. I got her used with grip for 1600 Euros in early 2013 and she is still my main camera although I still have my D3 which gets no use at all (pity, she is a hell of a camera) and my beloved D500 that does every thing better than the D600 except for some magic "analogue" feel in the tonality and rendering that comes from the recording chip.
I used the D600, D750 and D810 in parallel for a week of heavy shooting.
Result: The three cameras are very near together. Even compared to the D600 the D750 feels "amateurish" light weight, very "snappy" sound design, but she is also very fast and responsive plus she has exactly the same image recording chip as the D600. The D810 is a clear upgrade to the D800E, everything fell into place, she is a wonderful well rounded package, yet the price upgrade (today 2300€ vs. 700€ used @
ebay.de) does not justify the difference for me as I already had the D600. Sound design is much better, ergonomics feel much more professional. Tonality is better than in the D800E, but everthing is only slightly better than it is in the D600.
When I tested the D500 it was clear that she is a real upgrade to any camera I had before and that the next big thing will be the D850 or whatever she will be called. I got her immediately.
PS: Just now I noticed that amazon.de and amazon.co.uk do not list the D810 any more, only market place listings. Amazon.com listzs the D810 but only the "Black Friday Bundle" with grip for 2500 US$. I hope the D850 will be these soon. A D500 with full frame / FX recording chip and 42 MP? I would not hesitate to buy her!