I had the same problems of others with the small countries. Andorra was easier, as the map recentered over it slightly. Vatican, San Marino, and Liechtenstein were total guesses. A circle or arrow would have helped.
This is a great idea for a quiz but as the others have said you need to do something about the all but unseeable micronations. Also, the time is very tight given the need to zoom in and out and scroll up and down the list of countries.