The title of the film (and the novel it's based on) is, like that of many other works by Agatha Christie, a quotation of a piece of poetry. "The Moving Finger" are the first words of a well known work by the medieval Persian poet Omar Khayyam.
The Moving Finger writes; and, having writ, Moves on: nor all thy Piety nor Wit Shall lure it back to cancel half a Line, Nor all thy Tears wash out a Word of it. From The Rubiyyat of Omar Kayyam
Emilia Fox (Joanna Burton) is the first of the Fox family to appear in the series. Her cousin, Laurence Fox, appears in season two: The Sittaford Mystery. Her father, Edward Fox, stars in the season fifth title The Secret of Chimneys. Her mother, Joanna David, stars in the season six Greenshaw's Folly.