All of the Queen's equerries, assistants and servants address her as "ma'am" which rhymes with farm. However, it is well known that the real Queen Elizabeth II hates this and prefers being called "m'am" which rhymes with jam. As close aides to the Queen, they should really know this. Funnily enough the only person who gets it right is Sophie, who could be forgiven for getting it wrong.
When the Queen is in residence, the Royal Standard is the flag that should be flying above Buckingham Palace. In this film, it is the Union Flag. This should only fly when the Queen isn't at home. It used to be the case that the Royal Standard should be the only flag above the palace and when the Queen was away, there would be nothing. However, there was an uproar following the death of Princess Diana as Queen Elizabeth II wasn't home so there was no flag to put at half mast. Since then, it's the Royal Standard when she's in, and the Union Flag when she's away.
According to the postage date of one of the letters Sophie puts on the desktop, the events take place in September 1983. But when the Queen phones foreign presidents (suggested by the fact she tells to Nancy (Nancy Reagan) that she want to talk to Ronnie (Ronald Reagan)), she talks before with Boris. Assuming this refers to the Russian/Soviet leader, Boris Yeltsin was elected in 1991. Yuri Andropov headed the USSR at this time.