When Gunnar is talking to Sixten and Pompe, Sixten lays his newspaper on the table. It's folded and the header is upward. In the next shot the paper is up-side-down with the header downwards.
The train is said to go non stop to Berlin and therefore a character on the wrong train cant get off. However in 1945 you had to take a ferry to get to continental Europe. The Öresund bridge to Denmark was opened in 2000.
Set in December 1945, Gunnar writes a letter to his publisher Bonniers advising them not to accept Astrid Lindgren's first novel "Pippi Longstocking". Bonniers did in fact reject the script but in 1944. The novel was first published in November 1945 by a another publisher.
The edition of Wittgenstein's "Tractatus logico-philosophicus" that we see was first printed in 1992 (2nd ed. 1997), it could not be available at the time when the film takes place, 1945. The 1992 edition was a re-preint of an older edition from 1961. Tractatus was first published 1921, but with a German title, "Logisch-philosophische Abhandlung".
The doctor's watch has a date window, but the only wristwatch with a date window available in 1945 was the then newly introduced Rolex Datejust. The doctor's watch has a square case and is clearly not a Datejust.
When they get off the train in Berlin, an overhead contact line for electric engines is visible in one shot. However, there was no such installation in Berlin in 1945.