When Diego and Lila are descending the stairs at the commission home office a wide shot shows someone exiting the building with the pink dog mask worn by Cha-Cha in the first season. Diego appears to notice this as he stops on the stairs and watches the individual leave.
Lysergic acid diethylamide is better known as LSD.
John F. Kennedy was not the first Irish-American President, Jackson, Grant, and Truman also boasted Irish heritage. JFK was however, the first Catholic President. His Catholicism caused distrust among some voters of that time owing to concern that he might be influenced by the Catholic Church or the Pope, perhaps even above his duty to be loyal only to the people of the United States despite the Founding Father's and subsequent historical commitment to the "separation of church and state".
Dot says don't mess with case management. This is a pun on the briefcase used throughout series.