Tony should not blame rats for carrying the pneumonic plague. Rats carry the infected fleas that, upon biting a human, can transfer bubonic (not pneumonic) plague to that person. Pneumonic plague is generally transferred by being in close proximity to an infected individual.
Ducky asks Tony to perform a blood count by adding Methylene Blue to a blood drop on a slide. A blood count can never be done this way, and a blood smear stained with Methylene Blue would never look like it does in this scene - rather than a smokey blue color, this slide has been stained with hematoxylin and eosin.
The director says she has Top Secret clearance and is told the Chimera's mission goes beyond that. The director of any investigative agency is always cleared for everything, for obvious reasons. No director is ever limited to Top Secret alone.