To truly appreciate being an American, I believe one would have to live outside of America for some time. I haven't had the opportunity. Honestly I think that the idea that we're invincible is completely false. Empires come and go. What makes America different from Rome is the heart of the people. I love my country. I love the fact that I can protest my leaders if I wish. Many people I think have the false idea that "We're all Created Equal". That is a noble saying but I believe the truth is "We're all created with an equally blank slate". Many are born into poverty. Many are born with disabilities. A few are born well-off. Despite where you're born or to whom you have the chance to do with your life as you wish. One can waste life away doing nothing, serve others, or be self-serving. In America a person is afforded the opportunity to achieve a higher status. The government gives it's citizens the freedom to worship as they see fit (or not). I believe that people should have that choice.
America does have a violent past. There were a lot of wrongs as you pointed out. Vietnam wasn't very well thought out and slavery was/is unacceptable. The solution isn't in politics. Our Congress/Senate can pass laws all day but that doesn't mean that it will change anything. We as Americans (to Americans I speak) have to come to the realization that the future of our country rests in our hands. Our decisions are critical. What we choose to support is an indicator of where our hearts are at. The American Dream is shallow dream in the context of this entire tapestry we call human history. Life isn't all about the house with the white-picket fence, the perfect family, the perfect job, and the perfect car. Deep inside the human heart is a constant yearning for "something more". A poor farmer can have nothing but everything with joy in his heart. Don't get me wrong, the American Dream isn't a bad thing. What I'm saying is that this dream isn't the "it" thing. Is America different from other nations? Yes and no. I would hope that the American people would represent themselves in such a way that others would ask "What makes them great?" If we continue this attitude of pride and pomp we'll be no better than the Romans with their oppressive and crushing might. Lately I see that America has become a laughing stock. We're made fun of because our obesity and temporal consumer culture.