TobyBartels comments on Rationality Lessons in the Game of Go - Less Wrong
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Sorry for all the comments, I thought of some more things:
The "dark side" has an analogy in go. It is tempting to play moves that you know don't work because you think your opponent won't be able to figure out the correct response. It is usually not obvious to beginners that doing this is really holding them back.
I commonly hear beginners justify a move with the reasoning, "I played X because next I can play Y!" To which the response is, "But after you play X it's your opponent's turn. And he is not stupid and will prevent Y." Is there a fallacy this is analogous to? This reasoning is so widespread (there are more subtle forms) that one pro has said that the most important rule in the game is that black and white take turns playing.
This reminds me of the Go maxim that (for a given board position and abstracting away the parity) your best move is the same as your opponent's best move. This is rare in real life, where the situation isn't so symmetric. But it does teach you to look at things from your opponent's perspective.