Frank Frink gets shot by Ed in the right arm before the assassination attempt of the Japanese royalty. Yet, less than two weeks later, during a conversation with Arnold, Frank is in a tank top revealing his arm with no physical injury.
The offices in Berlin are shown to have push-button telephones in 1962. The first push-button telephone was not introduced until 1963.
Since The Man in the High Castle is set in an alternative reality the development of technologies may have happened at a different pace. They have supersonic airline-Service 14 years before the Concorde was introduced but other technologies stay behind the real world.
The long shot of Berlin shows several modern buildings like the Bundeskanzleramt (the Chancellery building), the Bundespräsidialamt (the office of the Federal President), the Bahntower, and the Kollhoff-Tower, all built in the late 1990s.
It is unlikely the song "Calendar Girl" would have been written in an alternate history where Nazi Germany occupied the east coast of the USA. Composer and singer Neil Sedaka is Jewish and lyricist Howard Greenfield was gay, and both were from Brooklyn.