Continuity mistake: Archer is at various times described as chief superintendent (a rank which wasn't introduced until 1949), superintendent and inspector. Nobody, including him, seems to know what his actual rank is.
SS-GB (2016)
1 continuity mistake
Starring: Andrew Bicknell, Michael Epp, Trevor White, William Meredith
Episode #1.4 - S1-E4
Other mistake: A major plot point is the rivalry between the Wehrmacht and the SS, who refuse to work together. After the explosion at the cemetery, it is the Wehrmacht who are explicitly described as rounding up and interning suspected resistance fighters, with the SS not being party to it. However, when Archer visits the internment camp, most of the staff are wearing SS uniform.