Aside from the issue of the fairness of the Moscow purge trials, or the truthfulness of the alleged confessions of the accused, the people shown standing trial together in the film in fact did not all stand trial at the same time. There were two such major show trials, one in 1937, the second in 1938, and the real life characters depicted in the film as being tried simultaneously were actually tried in separate groups at one of the two trials.
Davies and the rest of the diplomatic corps are shown watching the 1938 May Day parade through Red Square. Some time later, at the farewell dinner being held in Davies's honor, Litvinov is handed a communique stating that Germany had just invaded and annexed Austria (the Anschluss). In fact Germany had taken over Austria on March 13, 1938, a full seven weeks before the May Day parade that in the film precedes the Anschluss.
Davies is shown returning to America on board ship when he receives word of the signing of the German-Soviet non-aggression pact, and upon his return home eventually meets with several congressmen and tells them that war can be expected sometime within the "next two months", either in late August or early September. However, the German-Soviet pact was signed on August 22-23, 1939, and war began just nine days later, on September 1. Davies could not possibly have talked to the congressmen about a "two-month" timetable for war to come in late August or early September if he had reached the United States after the signing of the pact.