In Death of a Salesman, what failed opportunites did Willy miss by believing what he did?
The failed opportunities that Willy was not able to make the most from because of his obsession with his dream of making it big as a salesman mostly concerned his choice of profession. He felt he had to continue to work away at being a salesman, when in fact, he would have been far happier if he could just have acknowledged his tremendous gifts as a handyman and worked in a far less lucrative position out of the city in the country somewhere. Note how this is acknowledged in the Requiem:
There were a lot of nice days. When he'd come home from a trip; or on Sundays, making the stoop; finishing the cellar; putting on the new porch; when he built the extra bathroom; and put up the garage. You know something, Charley, there's more of him in that front stoop than in all the sales he ever made.
Linda remembers that he "was so wonderful with his hands," which causes Biff to say that his father "had the wrong dreams." Note in particular the way that Biff in the quote above said that there was more of his father in the stoop that he built "than in all the sales he ever made." This reflects the sense of missed opportunity and the tragedy that was Willy's life: because of his obsession with the American Dream and ever-elusive success, he missed out on living a happy and satisfied life where he could have earnt a living doing what he was naturally good at. Willy, because of his high expectations of himself, and his implicit belief that he could make it big if he worked hard enough and tried hard enough, was never able to see himself for who he really was.