What a great thread! Thanks to all the contibutors.
Some initial simple thoughts on some of the comments:
Anybody who can see a move or two ahead and is paying attention already knows tactics, but now I'm beginning to see why practicing them repetitively is so beneficial: because (among other things) it enables one to see the patterns more quickly. Pattern recognition. E.g., early in one's career we've all been on the receiving end of Nxc2+ where the knight forks the rook and king. And once you're stung by it, you never forget it, and that's something I *always* see. (Same thing with Bxf2+ or Bxf2# -- e.g., scholar's mate or fried liver) But now I understand that that's just pattern recognition. I don't always systematically scan the board the potential forks, or skewers . . . but (a) I will try to do more of that; and just as importantly: (b) with more familiarity with them (playing them over and over again in puzzles) it seems I will attain the level of recognition that I already have for the Nxc2+ fork, or the mate on f2/f7.
What a great thread -- thanks!
(BTW, one tactic that was in the chess.com lessons, but not in the table of contents of Bain's book, was the smothered mate. That was a new tactic to me -- and I find that I'm looking for that now. In a recent game I *almost* had one of those. I lost the game (I completely don't care at this point), but I counted as a victory for me because I saw the smothered mate as a possibility, and that was a level of play I wouldn't have had last week).
You could try the book "The Woodpecker Method"