Towards the end when Banning meets with the President to offer his resignation, he takes out his Secret Service badge and places it on the table. In the next scene when the President gets up to walk around the table, no badge is seen.
Trumbull appears a bit too old to be the U.S. President. It is however according to the constitution, that age 79 is the maximum age that a person has to be to be elected. The backstory on the series website states that Trumbull was elected at that age.