This site has enough dedicated Nikon users so that when you ask for information, you get it. Fast. Real fast.
I now have more than enough data to make a further statement about the 16-35mm. Your testing identified six lenses that clearly seem to have the problem. However, when all is said and done, that's a very small percentage of the number of lenses that were tested. Indeed, it works out to a low single digit percentage. In tech, single digit problems are common. You can't make tens of thousands of gadgets without some having issues. So I'm going to call this issue "within expectations for a complex product" and not a QA problem.
Obviously, if your lens has the problem and you take really long exposures, you'll need to have the lens looked at, unfortunately. One thing before you get too hot and bothered by that: make sure you do the tests with the eyepiece covered. I forgot to mention that parameter in my original sparse text, and I've had to have a few people retest because of that. Light can and will leak into your long exposure images via the viewfinder on most recent Nikon DSLRs.
Thanks to the hundreds of you who performed the test. I hope you don't mind that I didn't acknoweldge every email I received. I actually didn't think I'd get as many responses as fast as I did.
As for the D600 dust issue: still not enough data, but I also received plenty of comments about people's experience with this, as well. The trend seems to be this: some D600's came with dust, it doesn't clear off with built-in sensor cleaning, but when it is cleaned, the dust doesn't tend to recur at the same levels. Most people who reported using their D600s a lot (thousands of images ;~), seem to think that once the initial problem was handled, the D600 acts no different than other Nikon DSLRs. But I don't have enough data to say anything more than this seems to be the general gist, and this is all fairly anecdotal data (unlike a "is there a red streak" or "did it focus as well as Live View" test, people have differing opinions about what constitutes "some" versus "lots" of dust).
I have reports that the walk-in Nikon repair stations in Japan are cleaning D600 cameras for free when a customer shows up with this problem (usually sensor cleaning by the Nikon Japan repair centers is about US$12). Unfortunately, we don't really have such centers in the US.