The VP would not have a speaking role at the White House Correspondent's Dinner. Even if he did it would not be a humorless speech about politics.
It is stated that Tularemia is plague. This is slightly misleading. While one of the colloquialisms for Tularemia is Pahvant Valley Plague, it was not the cause of The Plague of the 1300's (aka The Black Death). The Plague was caused by Yersenia pestis.
Dr. Gordon gives the President's blood pressure as 129/85. However, he uses a manual cuff. The markings on a manual blood pressure cuff are all even numbers.
Agent Butterfield tells Dr. Gordon that they can withhold Cipro since they detected tularemia, not anthrax. The treatment for tularemia infection actually includes Cipro, since it is an antibiotic.