The Presidential Succession Act of 1947 specifies that when a Cabinet officer takes the oath of office as acting president, he or she automatically resigns the Cabinet post, so after the disability of President Dalton and the vice president to serve is removed, Elizabeth would be out of her job as Secretary of State. And this was just mentioned when the plan was to swear in the senator that was next in line.
Though the Presidential Succession Act of 1947 is silent on the issue, Amendent 25 to the Constitution (which supersedes an act of Congress) mandates that in order to resume the office of President after relinquishing it or the VP and cabinet for the relinquishment, the President must transmit a letter to the Speaker of the House and Speaker Pro Tempore to resume their office. Dalton would have to have sent such letter before resuming his office.
The newspaper Henry is reading at breakfast mentions President Obama in the headline instead of President Dalton.
The floor clock in the President's office was stopped at approximately 9:32. It was adjusted and a later scene showed that it was after 10:00.