Other mistake: John is promoted to Oberst Gruppenfeuhrer and assumes the uniform of such. He is soon after promoted to interim Reich Marshal. And then he is subsequently fully promoted to Reich Marshal. But he continues to wear the rank insignia of an Oberst Gruppenfeuhrer.
Suggested correction: John does eventually put on the insignia befitting a Reichsmarschall. It's safe to assume he didn't immediately put it on, either because it took a short time to produce new insignia and send it to him (they wouldn't stock insignia for a rank only a few people hold), or because he was still only acting Reichsmarschall.
Other mistake: When Matt and Claire are on the roof and Matt says "A dead guy, a guy I witnessed burn to death," Charlie Cox's natural English accent slips through. (00:41:35)
Other mistake: When Brian is using the right computer and thinking about the murderer of Paul Wilkerman, the computer screen is turned off. (00:31:40)