The movie depicts the Dalai Lama's coronation occurring after Germany surrenders in WWII and after China invades Tibet. The actual enthronement ceremony took place on 22 February 1940, (Iron-Dragon Year, 1st month, 14th day), long before the end of the war and the Chinese invasion. On 17 November 1950, the Dalai Lama assumed full temporal (political) power over Tibet which was more than 10 years after his enthronement ceremony.
(at around 1h 20 mins) A scene depicts communist Chinese troops stomping into the Holy Land. Unfortunately, the identification of "China" was wrong in the film. (1) The flag shown was for ROC (the short-lived Republic of China, founded by Dr. Sun Yat-sen, defeated by the communists), which was not the communist China's flag. Communist China's flag is all red with a few yellow stars. The flag shown in the movie is red-white-blue. (2) The Chinese government names, shown more than twice in the movie, said "Republic of China (4 characters)", whereas it should have been "People's Republic of China (7 characters)".
When Peter bargains with his watch about how much food they should get, he shows 3 with three fingers (the British, American, etc. way) and not two fingers and the thumb (the German/Austrian way).
When the Chinese troops attack the Tibetans at night, there's a mortar crew firing at the Tibetan troops. The officer in charge gives the order to fire in Spanish by saying "fuego".
Some of the Ghurkas who arrest Harrer in 1939 carry Sten Guns which did not exist for another two years.
The music of Lotte Lenya singing "Mack the Knife" while Harrer is in the British POW camp was not recorded until 1955, more than a decade after the time the scene took place.
When Harrer demonstrates abseiling (rappelling) in Lhasa, he uses a modern figure of eight abseiling device. In those days one used the "Dülfer" method or the "Karabiner-sitz" method.
When everyone is skating, all of them are skating on modern hockey blades. Some of the people can be seen with white plastic blade attachments.
Brad Pitt has a smallpox vaccination scar on his upper left arm. This type of vaccination, with the tell-tale scar, did not come into use until the late 1960s.
In the holy city of Lhasa, Heinrich converses with various native inhabitants in fluent English. It is highly unlikely that, in a city as isolated from the rest of the world as Lhasa, there would be so many people fluent in English or any other foreign language.