The BND (Bundesnachrichtendienst, Federal Intelligence Service) is shown to arrest various people. Being an intelligence agency, it has no jurisdiction to do so. Only the Police is allowed to arrest somebody.
After Carrie has been treated, Saul says that "Federal Police have dropped a net on the city". The Federal Police has no jurisdiction to do this, instead the State Police would be doing this.
When Astrid from BND threatens Laura with sending Numan back to Turkey, Laura replies "Turkey declared him an enemy of the state. They will execute him or worse". In fact, there is no death penalty in Turkey (By Law 4771 of 9 August 2002).
Alison is taken to Berlin Memorial Hospital. No such hospital exists in Berlin, Germany. There is such a place in Berlin, Wisconsin.
In this and other episodes, the characters frequently refer to "Hauptbahnhof Station". "Hauptbahnhof" is not a proper noun (even though, like all German nouns, it is capitalized)-it means "central train station", and thus that phrase is redundant. "Berlin Hauptbahnhof" would be more appropriate, as most large German cities have a central train station.