During Churchill's speeches in the Houses of Parliament the Members are shown sitting behind long desks which have never existed in the House of Commons.
Throughout the movie, there are various maps of Europe. Nearly every one of them shows Europe with post-WWII borders, specifically Germany and Poland. Austria and Czeckoslovkia are shown as independent, while most maps of the early 1940's showed them as part of Germany (at least western Czeckoslovkia). They avoid the anachronism of East and West Germany, but Germany is shown with its c. 1990 borders after (re-)unification, Poland is shown with its postwar borders which were drastically different than those before the war, and the German state of East Prussia does not appear.
On the table at one of the conferences there are miniature flags of the three powers. The U.S. flag used is the fifty-star flag, which did not exist until 1960.
Distance shots of Moscow show modern road vehicles
Exteriors of Moscow in summer months show bare trees and the characters are wearing heavy coats. The characters also wear heavy coats in Tehran in November, which is a winter month but where temperatures are generally in the high 50s or low 60s (Fahrenheit),
At the Yalta Conference, while the Big Three pose for their iconic photograph, Churchill tells Stalin that in Britain there are two parties, while in the Soviet Union there is only one. In fact, Churchill's Coalition government included three major parties, not two: Churchill's own Conservatives, Clement Atlee's Labour Party, and Sir Archibald Sinclair's Liberal Party. Both were in the Cabinet: Atlee was Lord Privy Seal and member of the War Cabinet; Sinclair was Secretary of State for Air.