At 30:07 when Tommy Lascelles mentions that the Baltimore Sun has picked up the Parker divorce scandal the Queen Mother asks "where?" But she would have known where Baltimore was because Wallis, the Duchess of Windsor was from Baltimore.
The Queen refers to the South Shetland Islands, the Falkland Islands and Ascension Island as "British Overseas Territories". However, in 1957 they were still Crown Colonies. They only became British Overseas Territories in 2002.
When meeting with Eileen Parker, Tommy Lascelles claims that he is reading "The Campaigns of Napoleon", by David Chandler. However, this book was not published until 1966.