Also, it's very strange that you can imply The United States started a war with good intentions with a straight face.

I always think of mistake as simply "to be wrong". Am I mistaken in my assumption?

Kind of, yes. If you're wrong intentionally, we have all sorts of other words for that, including trolling, propaganda, misdirection, incitement, lying, fraud, perjury, all of which have their own connotations for your intent. We wouldn't really call any of those situations a "mistake".