In this episode, a Nazi officer was shot. The hit distance is specified in "inch". They would use the metric system, ie. mm / cm / dm.
John Smith is an SS officer, but his cap badges are not those used by the SS. There is no Deaths Head badge and the main badge is as worn by the Wehrmacht (Army). However his Sturmbannfuhrer does have the correct SS cap badges.
The song "Edelweiss" is sung over the opening credits with the dark looming image of the globe engulfed by Nazis expansion in 1962. The song is presented as a traditional Austrian/German folk song. "Edelweiss" is a show tune created by two Jewish Americans, Richard Rodgers and Oscar Hammerstein, for their 1959 musical The Sound of Music. It is not a folk song, nor is it Austrian or German in any way shape or form.
There's a scene when Inspector Kido asks Frank Frink if he knows what "Zyklon D" is. While only Zyklon B existed during WWII, by 1962 the Nazis would have developed newer and more-sophisticated poison gases. This is indicated by the explanation that Zyklon D is "odorless and puts people to sleep", while Zyklon B was infamous for its odor and causing its victims to choke.
Although the pop song "Sukiyaki" was written in 1961, it was not released in the US until 1963. The plot takes place in 1962. In any case the song was written as a protest against the US military presence in Japan, so would not have been written in the alternate history where Japan won the war and occupies part of North America.
A 27-year-old young man enters a movie theatre in a no law zone, which has been abandoned for some 20 years, and not only he finds it powered, he's also able to operate the projector.