Episode #1.5 - S1-E5
Factual error: The facility raided at the end is referred to as belonging to the Ministry of Defence. Although Churchill held the post of Minister of Defence, the ministry itself was not created until 1946.
Factual error: Although he is openly an SD officer, Huth does not wear the SD insignia on his cuff.
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.