Isabel Radford says "Accidents will happen, even in the best regulated families." Morse attributes this to Mr. Micawber, while she thinks it was W.C. Fields. Actually, they are both right. W.C. Fields played Mr. Micawber in David Copperfield (1935) and said this line.
When Isabel Radford says "Must the evil that men do live on, or can it remain our secret?" she is alluding to Mark Anthony's funeral speech for Caesar in Shakespeare's play Julius Caesar (Act 3 Scene 2): "The evil that men do lives after them; The good is oft interred with their bones."
Upon finding Trevor's body in the mash vat, Morse makes a remark about "Clarence". That's almost certainly an obscure reference to the middle brother of Edward IV and Richard III, Clarence. He was famously found dead, "drowned in a butt of Malmsey" as legend has it. Legend further has it that Richard killed him (or had him killed) to help pave the way for his ascent to the crown, once Edward died and after the Princes in the Tower were dispensed with.
The song from which both Thelma Radford and Morse quote ("A bachelor gay am I, though I suffer from Cupid's dart.") is called A Bachelor Gay, and comes from The Maid of the Mountain, an operetta with music by Harold Fraser-Simson and lyrics by Harry Graham.