The historical context is appreciated, but I would recommend marking it as extra information. Many textbooks move extra content into boxes offset to the side of the page. Perhaps something similar could be done here. (The same goes for the cultural facts)
I like that the book explicitly states that it is essential to remember to include the tones when writing pinyin.
It's pretty smart to add a new diacritic for the half third tone, which I am guessing is borrowed from Vietnamese. The note that there are different signs for counting is also a practical mnemonic device. I like it a lot.
Overall, while I already knew some theory, I managed to learn a fair bit.