When Dr. Cronyn is describing high-functioning serial killers to the police, he refers to several American cases - "Starkweather, the Fairvale murders, and recently DeSalvo". Charles Starkweather and Albert DeSalvo were real serial killers, the latter apprehended only the year before the one in which this story takes place; however, "the Fairvale murders" is a reference to a famous film - Alfred Hitchcock's "Psycho". Fairvale is the small town outside which the Bates Motel stands in that movie.
The police search for a character called Nimmo, and have a great deal of trouble finding him. The name Nimmo is very close to the Latin word "nemo", which means "nobody."
In the pub, when PC Strange reminds Morse that it is his round, he makes his excuses and leaves. This was a running theme in the Inspector Morse series in which Morse always had someone else buy his drinks for him.
When Morse sniffs the pot of tea and exclaims "If that's the stuff the chimps drink, I'm a Chinaman," he is referring to a series of advertisements for PG Tips teabags which starred chimpanzees.
The piano music that Phillip Madison practices is the last movement of Beethoven's Piano Sonata in C sharp minor, Opus 27 number 2, known as the Moonlight Sonata.