I'm sure Harry Potter and the Methods of Rationality taught me some of the obvious, overt things it set out to teach. Looking back on it a decade after I first read it however, what strikes me most strongly are often the brief, tossed off bits in the middle of the flow of a story.
This was the very first lesson of LessWrong-style Rationality I actually started trying to deliberately teach myself as a result of my contact with HPMoR and the sequences. This is the powerful technique of actually Thinking By The Clock.
I used to call it Thinking For Five Minutes, but that technique name is a misnomer. It's practically a lie-to-children really. Sometimes I think for much less time, about thirty seconds. Sometimes I think for much more time, like a couple of days. Still, in the way that when you first learn martial arts you might stand in an awkward, stiff stance without turning or stepping I first learned to think by the clock in increments of exactly five minutes.
When I first went to a gym to lift weights, I did it with a friend. I didn't think it was going to work very well (I was a pretty skinny guy) but I wanted to humour them. I sat down on the bench they pointed me at, got a good grip on the heavy thing they wanted me to grab, and lifted it up and down for a while. When they said stop, I stopped. "That seemed kind of fast," I recall saying, "are we done?" Dear reader, we were not done. This pattern repeated when I first started going jogging with a different friend. I somehow expected the whole running thing to last, you know, until we got bored, which happened pretty quickly.