I don't know how much point there is in posting here now, after the day is done, but here are a few comments. Perhaps someone will see them.
The Shakespeare theme is certainly real. There's quite a few clues which are immediately
obviously connected to Shakespearean characters, such as 2d, 19d, 27d, 10a, 24d. However, if you add clues for which the solutions may be less obviously Shakespearean, but which do appear in the list of characters in one or other of his plays, there are just far too many to be chance coincidence. For example 11a, 8d, 13a, 17a, 22a, 16d, 6d.
For me, COD was 10a, with no competition. I guessed what the solution was at a very early stage, but couldn't see why, and kept coming back to it, and still not seeing why. Then suddenly it hit me, and I thought it was quite an amusing clue.
FOI 14a, LOI 7d.