Corrected entry: Tom Hanks has his overcoat stolen, but he has it back on later in the scene. Then he is back at his apartment asking for an overcoat.
Corrected entry: When Vogel (East Berlin Lawyer) is driving Tom Hanks, his car is a Volvo P1800. This car wasn't manufactured until 1963 and it was a Swedish automobile, restricted under the East German control.
Correction: The P1800 was made by Jensen Motors in West Bromwich in1960/61. The lawyer must have had very good political connections.
Corrected entry: In the opening scene the man is doing a self portrait from his image in a mirror, that is to his left. This image in the mirror shows predominantly the right side of his face. In the portrait, the image is turned with predominantly the left side of his face showing. Wouldn't it be natural for the artist to paint what he sees? That being a face oriented the same as what the artist sees in the mirror.
Correction: This is a question and not a mistake. Since we don't see the artist paint the whole picture, we don't know exactly how he posed for his self-portrait (or his skills in painting what he does not see) and the mirror to his left may just be for the final touches. In the painting he's wearing different clothes, so either he can paint what he doesn't see or did the majority of the portrait in a different outfit and could have had the the mirror/pose in a different spot.
Corrected entry: Aside from the fact that the Volvo P1800 coupe driven by the Vogel is a later mid-60s model, it also seems highly implausible than a lawyer from communist East Germany could be driving an imported sports car from the West.
Correction: Sweden was neutral during the Cold War, and had diplomatic ties to USSR during the 60's. Besides which, USSR/Russia has a long history of bringing in stolen cars from the West, often stolen from countries like West Germany, transporting them through satellite countries like East Germany, Hungary and so on, and selling the cars to well connected elites within the USSR.
Correction: Back in his room, he is not wearing a coat. He is wrapped in a blanket.