The photo showing Samaritan's agent Shelly Spencer in the White House also shows its Analog Interface, Gabriel Hayward, and Senator Ross Garrison in the background. This explains how Gabriel made it into the White House in Control-Alt-Delete (2015).
The sounds that the keypad makes that Root uses to access the room on the 9th floor is the same as the ones used in the movie "WarGames," that Matthew Broderick's character David records to break out of the infirmary.
The admitting physician at the hospital was played by John Preston. He is Carrie Preston's brother, and Michael Emerson's brother-in-law.
The key code Root uses to access the secure wing (222333) is the same one used in the movie "WarGames" when David is locked into the NORAD medical room.