Spencer went to move the chess piece at the end to have "one more game" with Gideon but realized he would have had a check mate and chose to let it be. In all his time playing Gideon at chess, Reid seldom - if ever - won.
Morgan reflects that early in his career with the BAU, he would be encouraged by Gideon to roleplay as the unsub; Gideon would say to him, "Okay Morgan, I'm the unsub. How did I do it?" This is a callback to the first two seasons, where this idea of submersive roleplay was one of the main traits of the Derek Morgan character, drawing a parallel to his supposed specialty in obsessive crimes. For a short time, he did it in every episode.
Gideon named his son Stephen after David Stephen Rossi. Gideon and Rossi started what was to become the B.A.U. in the late 1970s. Although both of their wives were pregnant at the same time, Rossi's wife, Carolyn, gave birth to a stillborn son, James, in April of 1979.
The closing quote recited by Hotch is the same as the opening quote by Gideon in S1/E5, Broken Mirror (2005).