Leo says he and Babish are men of Chicago. Yet in the first season Josh and Leo talked about him being a Boston Irish Catholic.
When the President and Leo enter Babish's office, the head of Babish's gavel is adjacent to his Dictaphone. In the following cuts, the gavel has flipped direction, with the head now opposite the Dictaphone.
Charlie notes that Zoey was 17 when she started college, however, in Ep 1.6, Mr. Willis of Ohio, he tells the men at the bar that she is 19.
When Sam is speaking with Ainsley in her office, the necklace holding her I.D. card changes location several times during their conversation.
Josh states that in 1939 England, France, and Austria were being pounded by the Germans. The UK was at war, not just England, also the period before France's invasion in May 1940 was called the phoney war specifically because hardly any action took place, so none of these countries were being pounded at that time. Lastly, Austria had joined with Germany in Anschluss in 1938 and so were part of the Axis and were not being pounded and would not have been even if the war proper had started.
When Sam expresses surprise that the Coast Guard officer being in a dress uniform, she replies, "We're required to wear the Class A's for any business on the Hill or in the White House." Only the Army has a uniform designated as a Class A. The Coast Guard and Navy equivalent is known as Service Dress Blue. A coast guard Officer would not refer to her uniform as a Class A.
The chess set in Babish's office is set up incorrectly. First, the lower right corner square for each player should be a white square, not a black one. Second, the kings and queens are reversed: the white king should be on the player's right, the black king on the player's left.