Hi there, thanks for writing.
Actually, the current version of Wp Store Locator is not built with country filtering in mind (that will change in the upcoming version 3.0, though). What the plugin does is, it takes a search term (a location name or a zipcode), and uses it as the center of a hypothetical circumference with the search radius that you have configured. Then, it retrieves all the store locations that fall within that radius and returns them, sorted by distance to the searched point.
So, the search term is meant to be, as I said, a zipcode or a location name, not a whole country, that is why it does not work well apparently.
You could, for example, create a category for each of your store locations where each category corresponds to a country, and then you could enable category filtering in the frontend, so only stores belonging to certain countries would be returned, but even in this case, you would always have to initiate a search with a location or postcode, and a search radius, so it could happen that not all the stores in the countries you are searching match the search criteria.
Please let me know if you need any clarifications about the above.
Best regards,