I do not agree with the statement that a 1300-1400 player "looks" for checks, captures and threats after opponent's moves unless you qualify that statistically ... I would say that a 1300-1400 player does it on 40% of all the moves and that goes up 20% every rating class, stopping at 99% for experts and titled players ( the 1% accounts for all those brilliant blunders we keep hearing every now and then).
Thinking NM Dan Heisman might say something along those lines as well. He often comments on how a 1600 or 1700 player might still not do it consistently on each move.
You might want to state that at Rating Level X, the player stops playing Hope Chess which more broadly addresses the checks/captures/threats sanity checking.
Just added a beginner categorization blog post @ http://www.beginchess.com/2009/08/02/anatomy-of-a-chess-player-from-beginner-to-expert/
This is a work in progress, and would love to have feedback from stronger players or coaches. I think this would be very helpful for beginners to intermediates so that they know what it is they need to work on in order to improve their chess.