"Love's Labours Won" is an actual lost William Shakespeare play, the text of which has never been located. Some scholars believe that it is not really lost, but is simply a working title for one of his romantic comedies such as As You Like It, Much Ado About Nothing, or All's Well That Ends Well, all of which have interchangeable titles which don't describe the play's content very well. Or even The Two Gentlemen of Verona, Twelfth Night, or The Taming of the Shrew, which all revolve around exhaustive efforts in pursuit of love.
When he emerges from the prop storehouse, The Doctor is carrying a prop that reminds him of a Sycorax (the evil aliens from the 2005 Christmas special, The Christmas Invasion (2005). Shakespeare tells him that he likes the word, and will have that off him as well. Sycorax is a posthumous character in William Shakespeare's play "The Tempest".
This episode originally aired a few months before the release of the final Harry Potter novel, making the J.K. Rowling references and the Doctor's line "Wait until you read Book 7." particularly memorable at the time.
In response to a flirtatious remark from Shakespeare towards him, the Doctor says, "57 academics just punched the air." William Shakespeare's Sonnet 57 is one of many believed to have been written to a man, and contains lines referring to time: "I have no precious time at all to spend,/ Nor services to do, till you require./ Nor dare I chide the world-without-end hour/ Whilst I, my sovereign, watch the clock for you."
In City of Death: Part Four (1979), The Doctor claimed to have met William Shakespeare, however his behavior upon meeting Shakespeare in here suggests he's never met the man before. Writer Gareth Roberts, in an interview, indicated that lines were written to reference the City of Death meeting, but were cut so as not to confuse new viewers.