Not to sound like a copout, but what I have learned from PGSM has not nnecessarily been from the show itself, but from this website because of PGSM. Despite the Hama jokes, I thought the food references were interesting in the diaries (I regularly drink soy milk - go Azama-san!). Kitagawa-san from time to time has something interesting to say about life in Japan (particularly in reference to how the "I" and "team" mentality is different in America in reference to baseball, as well as the evolving thinking in Japan's newest generation). Even though I don't have a worthwhile reply to post, that survey article Jay posted in Off-topic has stayed on my mind since I read it (though I would like to see a counter-balanced article).
As for the show itself, Im usually looking at the backgrounds (such as that wide shot of Usagi walking at the beginning of Act 17), looking to see how different Tokyo life is different than my own. I particularly look at the cars that we don't get here. It would be interesting to see a website that shows the various live locations that are shot in PGSM, and where they are located on a map.