I'm a bit of a fan of the disaster film genre so I was looking through the entry on wikipedia and came across it, I googled it and found it on google videos where I linked to, it's also on youtube but broken up into chunks.
In regards to the President leaving Washington, I think that that was SOP for a nuclear exchange. As soon as BMEWS picked up incoming contacts the President would be evacuated to Nightwatch (or NEACP [Kneecap])which would go up with Looking Glass and other airbourne command centers to ensure the continuity of government and command during the exchange. The president and whoever else they could get during the warning would then be put down at either Mount Weather, NORAD or Raven Rock depending on what had been hit and what hadn't. Chances are that there are facilities that aren't public knowledge that incoming ICBMs would miss. Once there the President (assuming he or she made it, if not then it would be whoever is still alive on the chain of command) would most likely be appraised of the damage sustained and inflicted during the exchange and would then attempt to contact the enemy leadership and based on the results of that, decide on whether to initiate a second strike via SLBMs.
Of course, if the missile comes in from off the coast via a lucky Yankee boomer, then the President might not be clear in time to escape the blast, in which case I do believe there are bunkers under the White House, but communications would be kaput and so the next person in the chain of command would have to take over until contact is re-established with the President to ensure that there is no interruption in the response.
You make a good point on the fake EAS in Countdown to Looking Glass Zachstar, I never thought of it that way.
