The amount of mustard on King George's hot dog varies between shots.
When Daisy walks in on Eleanor and the queen, the queen has both hands clasped. In the next shot, one is up and one is hanging at her side.
When FDR turns on the car radio, music begins to play almost immediately. In the pre-transistor era depicted, all radios used tubes and took many seconds to warm up before providing any sound.
The Navy bandsmen playing during dinner are dressed as officers--bandsmen in the Navy are enlisted sailors. The conductor of the band would have been an officer or warrant officer, but not the bandsmen.
The King and Queen are shown arriving at Springwood to be greeted by FDR. The real King George VI and Queen Elizabeth the Queen Mother accompanied Franklin D. Roosevelt and Eleanor Roosevelt to Hyde Park after several days in Washington, DC, arriving with the Roosevelts.
When the King and Queen of England drive through the gates at Hyde Park, and shortly thereafter when they are received by the president, the Marine detail would have been sharply commanded to raise their rifles to the position of "present-arms"--their rifles remain at their sides the entire time.
The King and Queen arrive to greet FDR at his home Springwood, but the building shown in the movie bears little resemblance to Springwood.
When FDR first shows Daisy his stamp collection, we see post-1939 models.
Several cars are shown with black New York license plates (with New York World's Fair lettering). These were actually 1938 plates which would have been replaced with updated orange 1939 plates very early in the year - well before the scheduled June 1939 royal visit.
This movie sets the relationship between FDR and Margaret Suckley (Daisy) as beginning after he was president. It did begin with a call from Franklin D. Roosevelt's mother Sara Delano Roosevelt, but it was in 1922, 10 years before he won the presidency.
When FDR calls for an end to Ish-ti-opi's ceremonial dance, Eleanor Roosevelt invites everyone to thank Ish-ti-opi in Cherokee. Ish-ti-opi (a.k.a., Wesley L. Robertson) was a Choctaw Indian, not a Cherokee. In any event, the word "yakoke" used for "thank you" is correctly Choctaw, not Cherokee. The Cherokee words for "thank you" are "wado" and "s'gi".
When Sara D. Roosevelt (FDR's mother) formally greets Queen Elizabeth (when she arrives in the dining room for the formal dinner), Mrs. Roosevelt calls her "Your Highness". She should have called her "Your Majesty", which is the correct title for a the King or Queen.
FDR shows Daisy a stamp of Victoria Falls in what was at the time Southern Rhodesia now on the border of Zambia and Zimbabwe. He tells her they are the highest waterfalls in the world. They are the largest waterfalls, but not the tallest. The tallest are Angel Falls in Venezuela.