While Amy and Josh are arguing about a treaty banning prostitution, Amy states that "the more toothless a treaty is, the more toothless it is". Josh refers to this as a "permeating syllogism"; however, Amy's argument is in fact an example of tautology (making an argument by repeating the premise), not syllogism.
The President is said to have been sued for "contributory negligence" for a remark that allegedly caused a driver not to wear a seat-belt, resulting in his being injured in a crash. Contributory negligence is when a victim of an accident has contributed to his own injury, not the action of a third party.
The F-117 is mentioned as part of an arms package to Qumar in exchange for base rights. Considering it spent much of its early career as classified and even in real life never had any foreign users, this is highly unlikely.