Monk is portrayed as being woefully out of shape and "hasn't run in thirty years" yet, there are several previous episodes where Monk does an extensive amount of seemingly effortless running.
When Natalie demonstrates her country dance, Monk re-dubs it a happy prospector dance, which is a clear reference to Howard's (Walter Huston) dance in The Treasure of the Sierra Madre (1948).
The fighters are named Ray Regis and Carlos Hiraldo. Their last names are references to talk show hosts Regis Philbin and Geraldo Rivera (Hiraldo and Geraldo are both pronounced the same). This adds an extra layer of humor to the big fight - Regis vs. Hiraldo/Geraldo - as noted by listening to the commentators during the fight who generally call the participants by their last names only.
The purple and red tracksuit Monk wears during his training sequence is similar in color and style to the bowling outfit worn by Jesus "The Jesus" Quintana in The Big Lebowski (1998). The Jesus was played by John Turturro, long-time friend and collaborator of Tony Shalhoub.
Monk is shown as being physically unfit. However, in Mr. Monk and the Marathon Man (2002), he is extremely fit and a fast runner.