The original 1939 novel has Luke Fitzwilliam as the chief investigator and does not feature Miss Marple at all.
The aria Lydia is listening to while she's crying at her dressing table is from Madam Butterfly. In Madam Butterfly Cio-Cio San gives up her child to her former lover and his wife.
Lyndsey Marshal who plays Amy Gibbs, went on to play Agatha Christie in Agatha and the Curse of Ishtar.
Both David Haig (Major Horton) and Anna Chancellor (Mrs. Horton) were featured in the same segment - Wedding Two: Bernard and Lydia - in "Four weddings and a funeral" (1994).
David Haig's character Major Horton's wife's name is Lydia. His character in Four Weddings and a Funeral married a character named Lydia.