Well said. Tartakover's remark is very reminiscent of the old military maxim that you don't win a war as much as your opponent loses it. Chess, being a wargame at heart, often emphasises this fact. 
Likewise, your observation that "the middle and end games are where the game is truly won or lost" is also spot on. I've been in plenty of losing postions that I ultimately won because my opponent missed an easy mate or grabbed a pawn/piece instead of staying focused on his attack.
Isn't it amazing how such a seemingly simple game as chess contains so many lessons applicable to all aspects of life?
I just got done losing a game that I was very sure I was going to win. I somehow managed to convert a two-pawn advantage to a one-pawn disadvantage out of my usual greed, impatience, and carelessness. The game isn't interesting enough to post here, but it did get me thinking about what may be the most valuable words of wisdom about chess that I have come across, Tartakover's remark that "The winner of the game is the player who makes the next-to-last mistake."
I'm sure that Tartakover's remark was at least partially tongue in cheek. After all he's also the player who made the similarly minded quip:
"A chess game is divided into three stages: the first, when you hope you have the advantage, the second when you believe you have an advantage, and the third... when you know you're going to lose!"
Joke or not, both of these remarks proved true for me in that game. It's was an instructive game for me, and I thought the lesson might be helpful to others, especially those who post with questions about the "best opening." While I have a fairly strong grasp of opening theory (at least with those that I play), I continue to lose late in the game. This would seem to suggest that the opening is at most something to survive, and that the middle and end games are where the game is truly won or lost.