The car chasing the escaping train with the secret items (towards the end) was a Citroen Light 15 (Traction Avant) "Big Boot". This model was only introduced in 1952. (See Wikipedia or Citroen Classic Car bibliography )
In the first episode, the main character is shown to have two scars on his chest. In further scenes, these scars have disappeared.
One is given the impression that there was a functioning Western alliance with the Soviets before the Nazi-Soviet Non-Aggression Treaty. In fact no definite agreement was ever achieved.
As Jean-Francois is being abducted from the cemetery, Marek runs outside, draws his pistol, then lowers the pistol to chamber a round. The sound of the bolt chambering a round can be heard. However, Marek had just shot the hostile agent who was following Jean-Francois. So the pistol would have already had a round in the chamber.
Kim Philby is shown in passing, working at some high level in British diplomacy. He did not in fact join MI6 till later. Was in Spain a lot of the time, acting as a pro-Franco journalist but actually working for the Soviets.
The mini series begins in 1937, several of the character are using the Walther P38 pistol which did not enter into service in the German army until 1938.