At the end of the previous episode, Kate takes Austin's coat. At the beginning of this one (which is set moments after the previous one ended), she is not wearing the coat, and the bodyguards are not carrying it.
Ambassador Desai tells Dennison & Kate that the quickest plane he can get them from Paris back to London on is a drafty RAF aircraft. But moments later, they are shown getting off a business jet in London.
Dennison is in his office talking to Libby while he's being urgently called to Trowbridge's office. He is changing his shirt into another plain white shirt. In the next scene, in the PM's office, he is wearing a white shirt with dark stripes.
CIA agent Park is speaking to the Ambassador, and refers to the British Prime Minister as the "head of state". This is incorrect as the monarch is the head of state in the United Kingdom.