The title refers to a 13th century German proverb. There are many versions over the centuries but the most common is: "For want of a nail the shoe was lost. For want of a shoe the horse was lost. For want of a horse the rider was lost. For want of a rider the message was lost. For want of a message the battle was lost. For want of a battle the kingdom was lost. And all for the want of a horseshoe nail." The meaning is that failing to see and remedy an initially small problem can lead to major, even catastrophic consequences.
Historically, Adolf Eichmann is best known for serving as "transportation administrator" for Jewish exterminations during the Second World War. However, in Nazi bureaucracy, he was actually viewed as a very minor and low ranking individual. The series depicts Eichmann as rising to the rank of an SS-Colonel General, which would mean Eichmann somehow surpassed all of his superiors in the alternate universe. Chief among these would be Heinrich Muller, head of the Gestapo, who is never seen in "High Castle", as well as Reinhard Heydrich who is shown executed for treason in an earlier season.
The women's clinic Helen Smith visits is called the Charles B. Davenport Clinic, which is named after an American professor of zoology at Harvard who was a proponent of eugenics and who was a supporter of the Nazi movement.
The tank at the Lackawanna mine is a Soviet T54, modified to appear more German.
Himmler wears his wedding ring on the right hand which is the German tradition.