There’s no such thing as “a contingency of experts,” “of French chefs,” “of Chinese ministers,” or the like. A contingency is something that might happen (“We must prepare for every contingency”). A group of people is a contingent.
If you’re not interested in something, you’re uninterested. “Disinterested” means that you have no direct stake in something, financially or in some other sense. A judge in a courtroom should always be disinterested in the proceedings, though they may interest him very much.
If you go to the museum to see a Picasso exhibit, you’re just seeing one painting or print or whatever. An exhibit is a single item. Think “Exhibit A.” An exhibition is a whole collection of exhibits, which is probably what drew you to the museum.
People use “flagrant” to mean obvious, as in “a flagrant error” or “a flagrant invitation.” It means something stronger than that, though — not just obvious but particularly offensive or objectionable. The aforementioned error and invitation are more correctly “blatant.”
San Francisco isn’t further from New York than Boston is and you didn’t run further than you should — it’s “farther” in both cases. “Farther” refers to physical distance, “further” to non-physical or metaphorical ones (“Let’s not take this argument any further,” “It is further stipulatedâ¦.”)