Technically, nothing is "wrong" with the family ambitions. Willy, Happy, and Biff all want to be successful in their own way. The problem arises in their perceptions - for Willy, to be "successful" is to be admired and wealthy, first for his own accomplishments and then for his son's. He plants the idea in Biff's mind that good looks, charm and athletic ability are all that are needed for this admiration. Willy gets wrapped up in the idea of the American Dream - that anyone can achieve great richness. However, Willy fails to understand or explain to his sons that these "riches" come with hard work.
This is why Miller uses the foils of Charley and Bernard, both reserved and hard-working men. Both of these men show a determination to do well in their work - as a result, they are both successful and happy. They aren't about flash - as shown when Willy is surprised that Bernard didn't mention his opportunity to argue a case in front of the Supreme Court. Charley's response is simply:
"He don't have to [mention it]—he's gonna do it."
This is in contrast with Willy, Biff, and Happy, who all talk a good game but never move forward with their plans.