During their phone call the President addresses the British PM as "Madam Prime Minister". While this is obviously an analogue of "Mr. President" the correct form of address for the PM (regardless of gender) is simply "Prime Minister" with no prefix.
In this episode CJ is woken up at 03:45 am EST being told that a British airliner has been shot down over Iran one hour earlier (02:45 am EST). Later in the SIT room Kate Harper explains, that the shot down 737 has the same signature as US spy plane RC-135, and at visual the radar on the back of the RC-135 might not be visible at night. However, when the plane was shot down the local time in Iran was 11:15 am, which means that it was broad daylight over Iran.
Lawrence Lessig says British Prime Ministers are weak because they are "subject to shifting coalitions". However, the UK's electoral system ensures that one party normally gets a majority in the House of Commons, meaning coalitions are very rare.
UK Prime Minister Grady (along with several other characters) refers to her country as "Great Britain", which refers only to England, Scotland and Wales and excludes Northern Ireland. She is the Prime Minister of the United Kingdom of Great Britain and Northern Ireland.