In the past I have suggested careful translation into modern English of the passages in Shakespeare that truly cannot come across intelligibly. However, an alternative would be the general acceptance that anyone who wants to get a full meal from a Shakespearean evening should read the play beforehand.
I would reverse those alternatives. Bantam Books used to have an excellent series of Shakespeare plays, extensively footnoted, informative introductions about the play and the history of its staging, and a wonderful forward by the late Joseph Papp. These, plus the BBC's video productions of the Bard's complete works, helped ease me into the rhythms of Elizabethan English, and to appreciate Shakespeare's genius.
Indeed, let Dr. McWhorter not lament that bits of Shakespeare are incomprehensible, but that so much of it is still intelligible. The English language morphed very quickly in the Middle Ages, so much so that by Shakespeare's time the English of Geoffrey Chaucer's Canterbury Tales was as obsolete as it is to us today. Yet the language has stabilized since then, by comparison. We still "get" Shakespeare in large part, almost as if the English language itself were wary of losing its ability to transmit the plays to living viewers. This is a cause for rejoicing. No, I don't know what some of those passages mean. I don't know who all those people in Raphael's School Of Athens are, either--but it's no barrier to feeling the genius of the art one is in the presence of.
You are very sensible, and yet you miss my sense.
Shakespeare, The Taming of the Shrew