Breakaway Pop Hit: "Mrs. Robinson" from The Graduate is an interesting inversion, as Paul Simon only wrote the chorus for the movie and they didn't bother finishing and recording the complete song until after the movie had become a hit.
Executive Meddling: A positive example of this is responsible for the duo's entire career. Short history: they first released "The Sounds of Silence" in 1964 in a completely acoustic version on their debut album. Said album tanked, then the two split and Simon moved to England. A year later, The Byrds spearheaded the folk-rock movement with their electrified covers of Bob Dylan songs. Sensing an opportunity, in June 1965 Dylan's producer Tom Wilson took the original backing track and overdubbed electric guitar, bass and drums, borrowing members of Dylan's backing band. (If you listen closely, you can actually hear the band go out of sync with the original recording at one point.) Not bothering to consult either Simon or Garfunkel, the new version of the song was released as a single and slowly climbed up to #1. Simon returned from England, reunited with Garfunkel and the two went on to more success.
Though they only agreed to if the execs promised they'd never pull a stunt like that without telling them first.
Old Shame: Somewhat averted. In their heyday they'd do a good-natured, not-entirely-serious version of their early Tom & Jerry hit "Hey Schoolgirl" in concerts.
Though it's a reference to Judas and those thirty pieces of silver, a metaphor used a few times by the duo.
What Could Have Been: Simon's 1983 album Hearts and Bones was originally conceived as a Simon & Garfunkel reunion album, but once recording began the duo started bickering and Garfunkel wound up leaving the project.