I don't have an issue with citizens of the United States of America calling themselves "Americans" because they are. Sort of like citizens of England can be called Britons (because of their living in the United Kingdom of Great Britain, and which is shared with Scots, Welsh and Northern Irish) or Europeans (although many don't consider them such because they are on islands off Europe and not part of the continental mainland). Citizens of the USA have every right to refer to themselves as American, but by the same token so do Canadians, Mexians, Argentinians, Colombians, et al. And what else are we supposed to call them? USAdians?
On the other hand, it does bug the anal retentive and precise part of me when people talk about the United States as "America" because America IS two continents, not just one nation.