I love Shakespeare and I love apologetics so approximately two hours after I first heard about this book, it was in my hands. I am nearly finished with it and I have to say it is a pretty solid piece of work.
I think for the most part the question is not so much whether or not Shakespeare is Catholic, the question is: was he a devout, heroic Catholic in the face of the violent religious oppression of the times. Statistically, the odds are pretty even that he would be either Protestant or Catholic but because he came from a Catholic family, associated with Catholic people, and was possibly educated secretly abroad in a school for Catholics, it seems more or less a no-brainer that Shakespeare was at least nominally Catholic.
I started reading the book with very low hopes. I have dedicated a lot of time debunking the "alternate histories" used to support rubbish like DaVinci Code and yes, unfortunately Asquith uses that very term a couple of times in her book (cringe). The problem with conspiracy theories is that they are mainly based on a LACK of evidence and any evidence offered to the contrary can be brushed aside as part of the cover-up.
There are not a few religions and organizations who use such dirty tactics to attack Holy Mother Church these days. In a way, conspiracy theories are too convenient -- you can believe them to the bitter end and never have to challenge them.
But this conspiracy theory is different because the point of contention is not as big a deal as arguing for the cause of your personal eternal salvation. The stakes are lower. The Cannon of literature is mostly Catholic anyway. And there are many facts about Shakespeare's background -- like his unusually high level of education for someone who never went to university. Asquith's book provides a lot of solid theories for these mysteries. Why has it taken 400 years? Does any Catholic seriously need to ask that question? How long has the Protestant population been grossly mischaracterizing Catholic practices as medieval superstition with no Biblical basis?
In a way, the story of Shakespeare's Catholicism is our story as well.
Even if you have no interest in Shakespeare's beliefs, the book serves as a very revealing historical socio-political overview of this very important time in the development of our culture. It is worth it for the history alone. In longing of Shakespeare in this book, we can see the original meaning of the concept of separation of church and state. It is clear this idea has its roots in the conflict of this time.
I am believer. It was reading works like Hamlet that helped convince me how wrong the doctrine of Sola Scriptura is: lip service alone is not enough, we must act in accordance with our heart or we become spiritually impotent.
I have started offering up petitions to Shakespeare just in case he is a saint. It would be nearly impossible to start his beatification at such a late date, but I have faith that the bard suffered for his Heavenly Father as much as for his art.

Just an example:
If you look at this poem by Shakespeare and keep in mind Catholic sacramentalism, relics, the Mass, the tradition of scholasticism and its own special language in reference to the Trinity - you can kind of see where she's coming from:
http://eir.library.utoronto.ca/rpo/display/poem185...

Not having read the book, I'm doubtful. How is it difference than all the bogus code claims in the Da Vinci Code? If people are putting symbols in art to covertly get out a message, chances are that the intended audience will understand the real message. If it takes 500 years to simply have one person get the message, most likely there is nothing there.

I've read part of the book and I'm convinced she's onto something.

"Did you listen to the audio clip on the web page?"
Yes, I did, DJ. Really beautiful!
I remember the firt time I heard a Mozart symphony recorded using the original insturmentation. It was a revelation. As is this. Man, I really wanna see this show!

Interest in Shakespeare's possible Catholic background has actually been a recurring issue for a long time I believe (the old Catholic Encyclopedia on newadvent.com even has an article on the question).
There has been interest payed to the role of Purgatory in Hamlet, for example, or the suggestion that Shakespeare associated with the Jesuit martyr St. Edmund Campion. And I think it's accepted that at least one of Shakespeare's parents were Catholic.
Stephen Greenblatt's new book, "Will in the World", traces some of these issues I believe (I haven't had a chance to read it yet) so that might be another place to go if you're curious about the question. It made a nice Mother's Day present for my mom (a former HS English teacher who loves Shakespeare).

Did you listen to the audio clip on the web page?

Very interesting, DJ! It's been known for some time in theater circles that the vernacular of Shakespeare's times was very similar to American Southern but I'd never heard that there's been an actual dialect developed.
I really wanna see this show!!

This is an interesting article I came across a while back.

'I am braced for flak, but we now know we have had the history from that period wrong for a long time because we have seen it through the eyes of the Protestant, Whig ascendancy who, after all, have written the history.'
I've not read Stripping of the Altars, but isn't that Eamonn Duffy's basic premise in that book? Interesting.
"This story caught my eye since I am currently reading through The Winter's Tale with a reading group, in preparation for seeing the play performed."
Asquith was on World Over Live with Raymond Aroyo just last Friday & I was listening in the car so I was only able to catch snippets when the signal was clear. I did catch her take on Winter's Tale (one of my very favorite Shakespeare plays - I was lucky to have performed in it) & Asquith's exegesis of the characters (especially Paulina) & of the final scene was fascinating. I think I'm going to add the book to my list!