The names of the main characters obviously refer to William Shakespeare and his wife, Anne Hathaway. As well, their first names are near homophones to those of the historical couple: Luella (Lu"Will"a) and Frank (Fr"Anne"k) Hathaway. The name of the senior police officer, 'Marlowe', is a reference to Christopher Marlowe, a playwright contemporary with Shakespeare. The assistant, 'Sebastian', most likely takes his name from the character in 'Twelfth Night'. See individual episode's trivia sections for more character names that come from Shakespeare's life and works.
The pub, The Mucky Mallard, is a play on the name of a pub in Stratford-Upon-Avon which is popular with actors, The Dirty Duck.
Filling the mid afternoon spot for gentle crime drama this series is made by the same production crew that makes Father Brown, The Coroner & WPC 56 (all of which have the same BBC timeslot).
The titles of the episodes are quotes from Shakespeare's works. See each episode's trivia section for the title's source.
The location of the outside of Shakespeare and Hathaway's office is the courtyard of the Lord Leycester Hospital in Warwick.