That is a summary of the answer.
“Do Americans have shared beliefs and values?”
What might be difficult or well-nigh impossible to define is anything uniquely American. Those values and beliefs are common to most of the developed nations, not just the USA.
You could ask “do humans have shared beliefs and values” and come up with the same answers. That doesn’t mean those values are always able to be lived and enjoyed but then the 99% activists would say only 1% of Americans can truely enjoy freedoms etc. The rest are in bondage (or so they argue).
A disdain for rules of grammar. 
Which I for one will never understand…
One trait that is nearly unique to the U.S., (although it may also be prevalent in Australia, and, perhaps, Alberta), are notions of rugged individualism and related traits, supported by a fair amount of mythology, (in the neutral, anthropological sense).
There is a reason that libertarian ideas, even when not supported by a majority, are more prevalent in this country than elsewhere. There is a reason why trade unions have traditionally had the most success among recent immigrant populations. American mythology supports the notion that the individual is paramount in a society. Associations of class or clan are not totally foreign to Americans–it is hardly an all or nothing proposition–but there is a recurring theme that the individual sets his or her own destiny, irrespective of any social connections and that the individual, in turn, owes nothing to any class or clan short of a fealty to the nation (and their local NFL team).
In the very first scene from The Wire, seemingly inexplicable behavior is justified by “Got to. This is America, man.”
(But I confess the scene leaves me confused. Is it valid? Caricature? Just a strange joke?)
I’d peg it as strange joke, “This is America we can’t discriminate (even against people that repeatedly steal our money)”. Good scene.
a related data point:
Every language and every country has a word for a farmer who raises cattle.
But only American English created the word “cowboy”. It really does represent a shared value, unique to America.
If every aforementioned shared belief/value were forgotten, the refusal to convert to the metric system would persist.
Americans share the belief that a person should be ‘presumed innocent until proven guilty’.
Sorry. We borrowed the word cowboy from the Irish. The specific duties differed, a bit, but the notion of a (typically young) man who tends cattle and has a bit of a wild streak in him was known and named in Ireland in the early 18th century.
As a matter of fact, from the War for Independence until the American migration pressed across the Mississippi, the word cowboy, in this country, was an epithet hung on loyalist (Tory) guerrillas of that war.
In addition, the gauchos of Argentina have nearly identical responsibilities and images.
The data point is related, in that our art and literature took the early Renaissance image of the knight errant and replaced it with the notion of the lone marshal or cowpoke who rides into town and defeats all the bad guys, (nearly) single handedly. The reality, of course, was that the American cowboy had rather more in common with feudal knights or samurai who fiercely fought to promote the interests of their (lord) rancher than with any literature-created noble loner fighting for justice. However, the knight-errant does a better job of promoting one of our basic myths, so that it where our literature has gone.
I am not sure what is “American” about that concept other than the words used. Despite various misunderstandings regarding the law in other nations, it is pretty rare that a modern societies presume guilt.
Not a total disdain, just a board thing.
Once again I will disagree. Serve on a jury on find out how many think “he” must be guilty, why else was he arrested.
Maybe we share the belief that we think we share the belief.
Caballero? gaucho?
Competition in all things. Lead, win, or get out of the game.
The exception is underdogs who buy into these values.
I’m not sure the question asked what Americans share that others do not.
Well, the OP’s (presumable) quote does ask about defining characteristics of Americans, and you can’t really define Americans without establishing that they aren’t “everyone else”. Given that, I think the presumption of innocence is a poor example because it’s virtually universal in Western society.
Perhaps not, but if we are examining “American” shared values, I would think that a love of country or promoting motherhood would be so widespread as to make them irrelevant to the discussion if everyone in the world shared those same values. Presumption of the innocence of the accused would seem to fall into that category. (It might be less prevalent for political trials in totalitarian and authoritarian countries.)
(And, as noted, while it is a nice legal principle in the U.S., it is hardly a universally shared value: just look at the numbers of people who have lined up to condemn either Trayvon Martin or George Zimmerman when no trial has even occurred.)
We really really really like our flag. Completely without regard for patriotism or symbolic value, we just plain like flying the flag. And putting it on signs, stickers, clothing etc. etc.