Lord Marbury calls the Queen "Her Royal Majesty". The Queen is always known as "Her Majesty". Her children and other royals are called "Her/His Royal Highness". The two are never mixed up.
The correct title for "Lord John Marbury" is in fact either "John, Lord Marbury" or just "Lord Marbury".
The shifting of US/Canadian borders wouldn't have caused Donna to lose her citizenship. There are many factors that determine whether or not one becomes a US citizen at birth, location being only one of them. For example, if Donna's parents were US citizens, she would derive her citizenship from them. The most that could possibly happen here is that Donna might gain a dual Canadian citizenship, assuming Canadian law allows for that.
Bartlet asks Abby what organ produces hydrochloric acid. She replied "pancreas" but the correct answer is "stomach"
When Abbey, Amy and C.J. go into a separate room to drink wine, Abbey tells the wine was a '95 wine who belonged to king Baudoin of Belgium. King Baudoin died however in 1993 so he could have never owned the wine. However, since the entire point of her rant is to call her husband "an enormous jackass", it's possible she's just making it all up to mock Jed's earlier pontificating about the evening's menu.
The premise that Donna's birthplace brings doubt on her citizenship,while comical, is astronomically unlikely. Donna is from Wisconsin, which does not border Canada. For this episode it is revealed that she was born in Warroad, Minnesota which is about 10 miles south of the most distinct border anywhere between the US and Canada (the 40th parallel). For Donna's birthplace to be in Minnesota, and for that place to be subject to a dispute or realignment of the national border, Donna would literally have to have been born in the equivalent of a swamp.
Lord Marbury talks to Toby about a fine Islay whiskey but mispronounces it "iz-lay". A person of Marbury's breeding and education would most likely know that it's actually properly pronounced "eye-lah" if you are from the UK.
In the opening sequence, while President Bartlett is working on a cross-word puzzle, he is stumped by a clue about an organ that produces Hydrochloric Acid, or HCl. Abbey responds that it is the pancreas, while it is in fact the stomach.
Lord John Marbury says he is "England's ambassador" - any British diplomat would have known the difference between Britain and England, and said "British ambassador".
During the playing of the Canadian National Anthem at Abbey's birthday party, President Bartlett not only does not render proper respect, he walks around and talks throughout. Even though it was meant to be a lighthearted jab at Donna, this would have been a serious breach of protocol at an official White House function.