Sandra's statement that the widow of a baronet changes her title and first name is incorrect. Sandra is not the daughter of an earl or a higher-ranking peer and thus would never be Lady Sandra. The wife or widow of a baronet is always Firstname, Lady Baronet'sSurname, never Lady Firstname.
In the black and white piece at the beginning the boy watches the young couple enter the house and almost immediately watches them draw an upstairs curtain, the couple could not have climbed the stairs that quickly.
During the black & white opening sequence, the female character's period-correct brassiere is removed to show tan lines from a very period-incorrect bathing suit.
Lady Annabel mentions being brought up in Kenya during the Mau Mau Rebellion. The rebellion took place between 1952 and 1960, by which time Annabel was an adult and had, in fact, already married Sir Freddie.
When Sandra is murdered, someone, presumably the shooter, throws pebbles at her window, most likely to draw her into view. However, Barnaby and Jones determine that the shooter was quite a distance away; the spot where they find the spent casing looks to be at least 50 yards (or metres, if you will) from the house. It's very doubtful someone could hit the window with pebbles from that distance.