Continuity mistake: When the Empress Dowager dies, she can't stand opening her eyes and closes them as the servant covers her face. You can see that through the white cloth.
Factual error: Buddy Holly is seen singing 'Cryin', Waitin' Hoping' at the Winter Dance Party. He hadn't actually finished composing this song, never mind recording it as a finished piece of work when he went on his final tour. This song comes from his final recordings 'The Apartment Sessions' which he recorded in New York and was finally released after his death, complete with added backing music and vocals.
Continuity mistake: Has a scene set during the Festival of Britain (1951). Oldman and Molina are shown at night on the South Bank of the Thames, ostensibly having just attended the Festival. In the background is a very clear view of New Zealand House, which wasn't built until the early 1960s, some ten years after the scene was supposed to take place.
Continuity mistake: When Donald Woods meets his wife again at the Lesotho airport, his hair has lost most of the black from being dyed, but once he's on the plane, his hair has become blacker again.