To my dismay, when I took today's issue and today's date, and worked backwards to see if I could match the issue numbers that I found in historical reprints, something was wrong. Except for very recent dates, the matching failed. Convinced that such a simple idea couldn't fail, I worked out a number of my "predictions" and compared the dates and determined the discrepancy, that is, the difference, measured in days. The mistakes weren't random - there was a pattern, with just a few jumps that seemed to occur in the past, until around the turn of century, when things really deteriorated.
It was really hard to figure out where to find good information to investigate this puzzle. There are a number of books about the New York Times, and even indexes of all the articles ever printed, but they seem to utterly ignore the issue number. There are books about business and art and history that, for effect, reprint a few covers of the New York Times, and if the reproduction isn't too bad, you can more or less make out the issue number. But where is the list of all the dates and issue numbers? Or better yet, a formula for getting one from the other?
Gradually, bits of the story surfaced. Sadly, the seemingly simple idea of a New York Times issue data calendar was marred by a number of historical "hiccups". The New York Times paused publication several times because of strikes, but valiantly published an inhouse dummy edition, to which issue numbers were assigned, and then they broke this perfect record for one strike in the 70's. That explained one problem. And before around 1905, the New York Times must have not numbered the Saturday edition, and somewhere around the Civil War the New York Times did not have a Sunday edition at all.
But the most amazing discrepancy occurred in the late 1890's when someone accidentally bumped the issue number up by 500! The second most amazing discrepancy occurred on 1 January 2000, when, in a misguided effort to "correct" the first discrepancy, the publishers subtracted 500 from the issue number. Now the mapping from issue number to date was not well defined! Purely by chance, if you know both the issue and volume number, you can still determine the date. But I suppose ridiculous irregularities like this occur for all human systems!