Give examples of Fitzgerald's view of the demise of American dream and upward social mobility.

The era in which The Great Gatsby is set was a time of growing wealth and opportunity in the United States. With growing wealth and opportunity came greater social mobility, with many people from relatively humble backgrounds getting a crack at the American Dream for the very first time.
However, as the American Dream became a reality to more people than ever before, it also had a baleful effect on those for whom it became almost an obsession. The headlong pursuit of wealth and social status corrupted many, and there are numerous examples of this in The Great Gatsby. In time, the American Dream declined, as the rampant selfishness of the 1920s gave way to the grim privations of the Great Depression. In the various characters of the story, we can see the seeds of the decline of America's foundational myth.
The most obvious place to start would be Jay Gatsby himself. If ever there was a poster boy for the American Dream and upward mobility, he is most definitely it. Originally hailing from a humble Midwestern background, Gatsby has transformed himself into a wealthy man, able to rub shoulders with the social elite at his famously lavish parties. Yet his success has come at a price. It is notable that he only got rich off the back of organized crime, through Meyer Wolfsheim and his notorious connections. Although this may well be an age of greater social mobility, there is a sense here that Fitzgerald is saying you always have to lose a little something of yourself to rise up in the world.
Even before Jay's criminal past is eventually revealed, he is still not fully accepted by the old money elite of East Egg. They are more than happy to mix with him socially and to attend his legendary soirees, but they will never accept him as one of their own. To them, he is still a parvenu—a vulgar, new-money arriviste who wears loud clothes and does not speak with the right accent. Rapid social advancement may be a characteristic of the Jazz Age, but there are still limits; the old money crowd are still in charge, and the likes of Jay Gatsby are never allowed to forget it.
Myrtle Wilson provides us with another example of this theme. She is a deeply unhappy woman, leading a boring, humdrum existence in the Valley of Ashes with her weak, unsuccessful husband. She craves a piece of the American Dream, yearning for a lifestyle of fancy clothes, ready cash, and high-class parties. That is why she thinks she is on to a good thing with her illicit affair with Tom Buchanan. He gives her a glimpse into a world that she could never hope to inhabit in a million years.
As with Jay, however, she does not truly belong in this world, and she is never accepted. Although Tom does not make much effort to hide his affair with Myrtle, there is still no way he would ever introduce his mistress to high society; she would be a monumental embarrassment to him. So Myrtle has to make do with an intimate gathering at Tom's bolt-hole in the city. Tom will give Myrtle a brief taste of life in the upper echelons of society but no more. She still needs to know her place. That is why the breaking of Myrtle's nose is so significant—she has started getting airs and graces, acting like she belongs among the upper-crust, so Tom feels like he has to put her back in her place.
Both Gatbsy and Myrtle Wilson are ultimately destroyed by their pursuit of the American Dream and their attempts at climbing the social ladder. It is not so much that they were wrong for wanting this, it is simply that they went about it the wrong way. They both tried to construct false identities for themselves in order to escape their less than distinguished pasts. In doing so, however, they lost sight of who and what they really were. For various reasons, they just could not be themselves.
That privilege remains with the East Eggers, the Tom Buchanans of this world. They can carry on with their lives safe in the knowledge that they will always somehow land on their feet no matter how hard times get. In the meantime, those corrupted by the American Dream, those less fortunate and less privileged in life, are forced to pick up the pieces of their broken lives and somehow figure out a way to move on.