At the White House Christmas party, the Crown Prince and Princess take the same drink offered to them by the servant. Moments later the Crown Prince is holding a completely different drink and glass.
In the scene where the Crown Prince and Princess accept drinks from the tray, there were two each of two different types of drinks offered. The princess takes the taller one and the prince the shorter. Thus they correctly are shown with those drinks moments later.
The Pearl Harbor scene set on December 7, 1941 shows two small aircraft carriers. One of the reasons the attack at Pearl Harbor was a strategic failure is that the American aircraft carriers were not present during the attack, but out at sea.
Missy LeHand's collapse and stroke occurred in June of 1941, not after Christmas of that year.
The attack on Pearl Harbor is depicted in a completely unrealistic way. Warplanes are simply flying over the harbor, and the ships docked there are just sitting there. In reality, the Japanese forces attacked the ships immediately. Their plan was not only to sink as many ships as possible but to do so before the ships had a chance to get out of the harbor so that the harbor would become unusable. And even though the attack was a surprise, the crews of the American ships and the antiaircraft batteries on land wouldn't wait for the Japanese planes to fly over before opening fire on them.
The aircraft carriers and cruisers seen in the Pearl Harbor scene on December 7, 1941 are obviously modern and not WW2 vintage.
When Fleischer is preparing to depart from a London airfield, there is painted on the underside of an aircraft wing, "USAF." During WW2 the United States air forces were still a division of the Army and designated "United States Army Air Force," or "USAAF." It did not become the separate United States Air Force (USAF) until 1947.
When Norwegian troops are shown at an Allied airfield, a C-47 is briefly visible with "USAF" painted on the underside of one wing. Until 1947 the air service was part of the US Army. During WWII it was called the Army Air Forces, thus the plane's markings should have read "USAAF".