The music that Randy's MP3 player keeps playing is the song "Stay Loose (Lyrics Born Remix) " by Jimmy Smith on the 2005 compilation album Verve Remixed 3. This song was not included in the show's credits, however.
The outside of the house of Peter Magneri (Alfred Molina) is the same as the house used by Tony Vivaldi (Anthony Quinn) in Last Action Hero (1993), which also starred F. Murray Abraham, who was Tony Shalhoub's co-star in Thir13en Ghosts (2001), and is mentioned by Marci Maven in Mr. Monk and His Biggest Fan (2007).
Trypophobia is the fear of round things that Monk specifically denies having here. Interesting in the context of this story line. He is non-committal on the fear of clouds (nephophobia). Oddly, genitophobia does not crop up in the conversation at all.