As the episode is about to close and Smart has all the suspects in his room, watch the small mirror on top of the dresser. As #99 moves into position, we see her bare feet in that mirror. This was a result of trying to keep her at approximately the same height as #86, as Barbara Feldon was indeed taller than Don Adams.
Per the title, the song "School Days (When We Were a Couple of Kids)" was written in 1907 by Will D. Cobb and Gus Edwards about a couple looking back sentimentally on their lifelong friendship and their days in primary school.
The character of Dimitri was played by Philip Roth, who bares a striking resemblance to the character Gru from the animated film Despicable Me.