In fact, the process is biased
against the two daily puzzles having words in common, and consequently there are probably fewer common letters between the puzzles than would otherwise occur.
The issue was raised in the forum in 2007. (Incidentally, the forum last week passed, without fanfare, its 4th anniversary: the first posts were on 4 February 2007.)
I reported
here that I had changed the puzzle to reduce, but not eliminate, the incidence of daily puzzles with common words. The change I actually made was along these lines: after the selection of the letters for the second daily puzzle, there is a check to see if the proposed letters of the two puzzles would allow any words in common at all. If so, the letters for one of the puzzles are re-selected. However the test for a possible word overlap is only performed once, so it can happen that the re-selected letters may also permit some words in common with the other puzzle.
So the check is not directly on letters in common, but on the possibility of words in common, taking into account the letter that must be used in every word. In theory, two puzzles could have 7 letters in common and still not be able to make any words in common - if the mandatory letter of each puzzle is not part of the other puzzle.
I said in the original post that there were common words about one day in five. The change I made then should mean, I think, that common words occur now only about one day in 25. I haven't actually checked the past puzzles to see if that is true.
However, to get back to your question, Pat, there still might be more common letters between the puzzles than would happen if the choice of letters were completely random. But it isn't. Firstly, the nine letters have to make a reasonably common nine-letter word. Secondly, the set of letters, including the designated mandatory letter, must be able to make a fairly large number of common words. Both of these requirements tend to favour the selection of the letters that are most commonly used in English words: ETAOINSHRDLU, or thereabouts. So, since any set of candidate letters is likely to favour the high-usage letters, the chances of any two puzzles having a number of letters in common are quite high.
TRex, regarding the issue of the same nine letters re-appearing too quickly, the rule currently being applied is that they must not have been used in any daily puzzle in the past 12 months. But the exact same puzzle, with the same letters and the same mandatory letter, must not have been a daily puzzle in the past three years.