The name of the German-occupied "Greater Nazi Reich" doesn't really make sense. "Nazi" was a German colloquial abbrevation of "national socialist" and was never officially in use during the period of the Nazi rule in Germany - officially naming a state like that would have been like officially calling the USA "United Yank States" or the USSR "Commie Union of Russia".
In the TV show: as in the book, characters whose surnames are traditionally associated with Jewish heritage change their names to avoid persecution, even if they aren't actually of Jewish descent and/or don't personally identify as Jewish, with Frank Frink (originally Frank Fink) a prominent example discussed in-universe. So how the heck is no-one talking about the fact that the Obergruppenführer's son is being treated by a doctor named Adler?
Genius Bonus: In "Revelations", it is shown that the secret "Baynes" tries to get over are nuclear fusion formulas.
Follow the Leader: The first few editions of the book had covers with a rising sun and a swastika side-by-side, sometimes dividing a map of the United States in half. Simple, direct, and to the point, right? But in the late 80s, after the release of the Cult Classic PKD adaptation Blade Runner, all of a sudden we get this◊. Although the book mentions that Nazi technology in rocketry has advanced, nothing in the book even remotely suggests the San Fransisco of this alternate universe is the kind of cyberpunk metropolis Blade Runner popularized. In fact, when Tagomi crosses over to our world, it's suggested the San Fran of the book is even less industrialized.
Hilarious in Hindsight: The way the Japanese fawn over the tritest American kitsch in the book is funnier now, after the rise of anime and manga fandom in the United States, some members of which do the exact same thing to Japanese culture.
Nausea Fuel: The Nazi doctors inventing new uses for dead bodies, such as using the joint of the big toe as a mechanism for a lighter.