In 1972, Monk mentions that he and Sherry are both fans of The Patty Duke Show (1963) and he has a photo of Patty Duke in his locker. Duke's son Sean Astin later played Paul Buchanan in Mr. Monk Is at Your Service (2007).
The flashback scenes take place in April 1972.
In the Young Monk flashback, a school bully sarcastically calls him Columbo, a reference to the detective series "Columbo (1971)" that this show shares many attributes with, including a quirky and eccentric homicide investigator who people look down on until realizing his brilliance.
When Natalie is looking at Monk's picture in his junior-high yearbook, the name listed right under Adrian Monk is Robert Mueller, which happens to be the name of a former FBI director who served from 2001 to 2013. In 2017, Mueller was appointed Special Counsel for the United States Department of Justice, where he served two years.
'Stairway to Heaven' was never released as a single; young Adrian is presumably referring to buying the 1971 album it is on, Led Zeppelin IV (or Four Symbols) although he just uses the name of its most famous track.