The Oscar Wilde quote comes from his 1895 play The Importance of Being Earnest and reads: "To lose one parent, Mr Worthing, may be regarded as a misfortune; to lose both looks like carelessness."
In the original story "The adventure of the Noble Bachelor", Inspector Lestrade was investigating the case. Since Colin Jeavons, who played Lestrade in all of Granada's Sherlock Holmes productions, wasn't available, another police detective took his place with Lestrade's absence being explained as him being at a spa.
Anna Calder-Marshall (Lady Helena / Agnes Northcote) is the wife of David Burke, who played Watson in The Adventures of Sherlock Holmes (1984).
There are two different actresses, both named Mary Ellis, with a great age gap between them. The younger one appeared in this episode, the older one in the next.