These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Americans Hate Tingle: "Hate" may be too strong a word, but during its original run in 2010, viewer interest in this show in the English-speaking world dropped dramatically after Episode 6... because all but one fansub group stopped working on it. It took months for translations of the latter half of the series to come out (by which time the show was already over), because the vocabulary and concepts used * such as deterrence theory, nuclear physics, and extensive discussion of very obscure literary authors such as Rampo Edogawa were so difficult to translate that it discouraged a lot of fansubbers from even trying their hand at it. Most people were quite surprised to find that an official English release was put out by Sentai Filmworks, as general opinion was that this work was too obscure and the subject of too little interest to Westerners to be profitable.
Fridge Logic: Should they really be speaking Japanese so loudly in China the year being what it is?
Yes, seeing as how the Japanese military was one of the major occupying powers in China in the inter-war years. It's like having Englishmen speaking English in Hong Kong in 1931. Shanghai was one of the most cosmopolitan cities in the world, with significant numbers of White Russian refugees, Germans, Italians, Americans, French, British, Japanese... pretty much every major power was represented in a large way. Moreover, in 1931 Japan had not yet launched its full-scale invasion of China (that happened in 1937) so Chinese attitudes to Japan, while not friendly, were not to reach the fevered pitch of hatred that came later.
That being said, they were getting there quite quickly. By this point in time even the warlords were starting to get united behind the idea of opposing Japan at the expense of putting aside their own rivalries, and Chiang was becoming incredibly unpopular for continuing to pursue the war against the CCP at the expense of confronting the Japanese. On top of this, it was never quite clear that the Japanese *weren't* in the process of launching a full scale invasion since they were continuing to advance furiously in the Northeast and the situation in Shanghai itself was ratcheting up towards a localized *war* between the KMT and the Japanese. So it probably isn't that wise to be doing it so loudly.
They Wasted a Perfectly Good Character: The common criticism on the show is the lack of character development since the show focused too much on the plot. Though the main characters have some interesting backstories, the one who suffers the most is Natsume who doesn't have much focus other than being Yukina's servant and having a sister back home.