If this is so, why then are there still plenty of problems where the initial position is completely winning, e.g. #19656? Did you not re-run the old problems through the new versions of the generator?
I'm not sure I understand your point with #19656. This position is completely winning because there is a mate opportunity , this is the whole point of the position. If you want to remove positions like this then there will be no mates in the problem set. Based on material balance white was actually behind at the start of the tactic which is why this position is allowed, if white was already say a queen up then this position would not have been allowed.
[Minor edit: The above statement was not quite true, currently the "already won" heuristic only applies to non-mate positions, there are technical issues in applying it to mating positions which I'm currently testing a workaround for (but #19656 still looks ok to me)]
Perhaps my original heuristic 2 was not strong enough. One could tighten it by demanding that the move (or sequence of moves) is the only one which either leads to a clear advantage or mate, or avoids a clear disadvantage. In this sense, the difference between winning the queen or rook (your example) is marginal, as both lead to clear advantage.
This idea is also already in place :-) if the second best move is also very good, then even if the best move is winning the generator will reject the tactic. Of course there is always tweaking around exactly what "very good" means and perhaps this parameter could be stricter than its current setting (and this heuristic only applies for non-mating tactics).
Perhaps one can learn from other sites: I found the problems at
http://chess.emrald.net/ quite useful (though your web interface is superior

).
CTS certainly has very good problems. As it seems to use tactics that were actually played in real games it has less of the "only a computer would see that" positions than Chess Tempo. However CTS also has a lot of positions which finish before the main point of the tactic has played out. Chess Tempo also has some of these , but subjectively I feel CTS has more.
As mentioned previously, problem generation is under ongoing improvement. Hopefully as the generator involves the Chess Tempo problem set can have all of the CTS strengths and less of its weaknesses :-)
Regards,
Richard.