I was reading the prefaces to the first and second editions of the book, which I assume must be in most published versions of this.
In the first preface, Walpole had assumed the guise of a translator who had 'found' the manuscript and was just translating it, but also arguing in favour of the veracity of the events in the manuscript. A note in the edition of the book I am reading said that at that time in the 18th century, many people looked on novels as a waste of time, as in 'Why should I waste my time reading about something that never even happened?' and that the preface was to lend an air of authenticity to the book to try to persuade people to read it despite that attitutde.
That reminded me a lot of the 'defense of the novel' in Northanger Abbey.
In the second preface, it seemed clear that Voltaire had criticized Walpole's work, and so Walpole dropped the translator persona and wrote as himself. From what I understood, one of Voltaire's complaints was the way that Walpole made his 'domestics' speak and act, and that there was no place for comedy in a serious work.
In his own defense, Walpole argues in the second preface that if it was good enough for Shakespeare (like the gravediggers in Hamlet, for example) then it was good enough for him.
This got me noticing some of the little incidents or devices Walpole included in the story that I can only suppose were in imitation of or in hommage to Shakespeare, such as the ghost beckoning to follow him (like the ghost of Hamlet's father does) or the name of Isabella. Isabella is the virtuous heroine in 'Measure for Measure, pursued by the lecherous Angelo.