The tune Peter Tork plays on the banjo while Davy Jones is packing is Johann Sebastian Bach's "Jesu, Joy of Man's Desiring".
The Champ is loosely based on Muhammad Ali (formerly Cassius Clay, as name-checked in Your Friendly Neighborhood Kidnappers (1966)), who taunted his opponents in rhyme before fights.
The "wise man" quoted by Davy Jones is comedian Bill Cosby; specifically, "A Nut in Every Car" (about derelicts riding the subway) from Cosby's first album.
Aired three days after The Monkees' fateful showdown with music supervisor Don Kirshner over the group's involvement in performing on record; the boxing theme took on disturbing irony when Michael Nesmith famously punched a hole in the wall upon being provoked by studio VP Herb Moelis.