There are a number of themes in this book, but to me, the main theme is the idea that hopes are often raised, only to be dashed. I think that this is one reason for giving the book the title it has -- the whole concept of picture brides is one with the potential for this kind of disappointment.
If you think about it, every dream that Hana has pretty much lets her down. Taro is not the way she dreams of him being. She dreams of having a son and has a daughter instead (and has a hard time understanding her daughter). She thinks America will be a country of freedom, but as a Japanese, she does not really experience this.
There are other themes, but I think this is the main one.