The moon waning as Sano trains was some surprising attention to detail. The moon really was waning in the second half of May 1878, with last quarter on May 24.
The first conversation with Anji during training was good filler. The second one, I'm not so sure, but it worked.
There are four acts that make a monk immediately fall from the religious life and make him ineligible to ever become a monk again in this lifetime: sex, murder, grand theft, and false spiritual claims. Anji didn't fall from desire, so what did he do? (Don't answer that.)