Mistakes Hanna made
Before you assume that I hate Hana, I should state that the movie makes it clear of all the tribulations that Hana endured raising her two children, which gives her the admiration and respect of the viewer; but anyone could admit there are a few areas in which Hana made mistakes. It doesn't mean she's bad, it just makes her imperfect, more human, and argualby a more relatable character. For me, her two biggest mistakes would be:
Forcing Yuki to apologize to Sohei without considering that her daughter may have been provoked, and trying to subtly steer Ame towards being a human despite moving to the country to give her two children a choice between the two fates.