Episode #1.3 - S1-E3
Factual error: Dunn says he's researched at the British Library. It wasn't called that until 1973. Before then it was the British Museum Library and always referred to either as that or simply as the British Museum.
SS-GB (2016)
1 factual error in Episode #1.3
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.