While in uniform, Captain Connolly and Joe Blake are shown to hold the SS-Hauptsturmführer rank by their shoulder straps/marks. However, the collar badges only depict three silver lines beneath the three silver pips, whereas, the SS-Hauptsturmführer rank should depict four silver lines, or two double silver lines beneath the three silver pips.
Joe Blake pistol whips the Yakuza leader and knocks him out while stealing the film. However, when the Yakuza leader meets Inspector Kido later, there's not mark, bruise, swelling, or any other sign that he take a blow to the face/temple during the escape.
The soundtrack includes the theme song from "Town Without Pity." The song was the title track of the 1961 film, concerning American soldiers accused of raping a German girl in occupied Germany. This film, and hence the song, could not have existed in the time line of "The Man in the High Castle".
At the end of John Smith's visit to Erich Raeder, the wide shot (10:39) shows a modern aluminum clip board in the lower right which was not introduced until the mid-70s.