I love Aaron Sorkin and have used that clip several times myself. What Sorkin doesn't say is that in many other nations, he, the actor who said it (Jeff Daniels) the producers, the television network, and all of the extras would be incarcerated.
What Sorkin (and yourself) also have forgotten is that greatness doesn't mean being "#1", the ways and means are just as important. We have a problem with poverty. We have a problem with inequality. We have a problem with wealth disparity. We have a problem with race. We have a problem with trust.
But for all of the problems we have with poverty, inequality, wealth disparity, race, and trust; we do not have people dying of hunger, a caste system, poor who cannot afford basic necessities on a chronic basis, race wars or shooting wars on any kind. You want to see what a "not so great" place looks like; check out Samolia. Check out Brazil where the average income is something like $700 a month. Check out China where communal toilets are still the norm.
America is Great. Americans forget just how much.