The board is made up of a handful of critics for major publications (in New York usually) who see everything in New York and often travel to see major regional works around the country anyway, to review them for their papers (both Brantley and Isherwood often review shows in Chicago, LA, Williamstown, London, even Pittsburgh -- when new August Wilson works would premiere in the past).
And to follow up on what Jon said, The Pulitzer's reputation for "excellence" rests ENTIRELY on its journalism awards. In that field they are still considered one of the highest honors one can receive. In theatre however, The Pulitzer is something of a joke in many circles, having made one bone-headed decision after another through the years (Harvey beating out Glass Menagerie; No Award instead on Virginia Woolf -- which caused several members of the board to resign that year); Anna in the Tropics, which none of them had seen and had only read the script of when they voted for it and then they all panned it when they saw it on Broadway a few months later). Obviously, no playwright or producer would turn down a Pulitzer (simply because it "sounds" prestigious), but if you're looking for a respected arbiter of the best of theatre in a given season, look to the Obies, Drama Desks, and NY Critics Circle Awards, all of which have very long and consistent history of singling out excellence.
As for this year (or last year, actually), 2005 was an incredibly weak year for new American plays. I saw several dozens (probably every major opening at all of the not-for-profits in town, and many of the commercial openings on and Off and even off-off-Broadway) and I think I would give "No Award" this year. Bridge & Tunnel is solo showcase for Sarah Jones mimickry gifts, not a great stand alone piece of writing. I don't think RABBIT HOLE is eligible (the deadline was December 31st, but it opened in January, 2006 -- I suppose the script could have been submitted by itself, though).
I liked ORSON'S SHADOW a lot, but wouldn't give it a Pulitzer. Same with Craig Wright's ORANGE FLOWER WATER and Douglas Carter Beane's THE LITTLE DOG LAUGHED, though I enjoyed them. I can't imagine them going with any of the musicals from last year -- SEE WHAT I WANT TO SEE, SPELLING BEE, LIGHT IN THE PIAZZA (which could possibly have eligibility problems given the Italian setting, but the central plot concerns Americans) etc...
IN THE CONTINUUM certainly has the kind of gravitas the Pulitzer Prize is looking for in the works they honor (concerning the impact of AIDS on two young black women -- one here and another in Africa; it's a little formulaic, but very effecting). There might be some sentiment for Wendy Wasserstein's THIRD, given her recent death and it certainly was a worthy effort from her. My personal favorite, Charlie Kauffman's HOPE LEAVES THE THEATRE (a quirky, surreal quasi-radio play performed by Meryl Streep, Hope Davis and Peter Dinklage), has no chance I'm sure -- it's probably too "out there" and "different" for the jury.
In the end, I think I'd be quite happy with "No Award" this year.
"What a story........ everything but the bloodhounds snappin' at her rear end." -- Birdie
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"The Devil Be Hittin' Me" -- Whitney
