The film differs from the book in several ways. Most significantly Miss Marple isn't called in until about 80% into the book.
Just before the meeting of the maid and her boyfriend on the bridge, there is a view of Willie Lott's cottage in Suffolk, famous because it appears in John Constable's 1821 painting The Hay Wain.
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 stanza of a well known work, The Rubaiyat, by the medieval Persian poet Omar Khayyam.
This movie, based on a novel by Agatha Christie, was directed by Roy Boulting. His brother Peter Cotes (born Sydney Boulting) directed the original production of Christie's famous play "The Mousetrap" in 1952.