In Death of a Salesman, what mistakes did Willy make at the beginning of the play where his memories flow back to when Biff is in high school?
Willy made many mistakes. These early memories concern mostly his parenting mistakes. Early in the play, when he remembers Biff and Happy as teenagers, he advises Biff to be "careful with those girls." He tells Biff not to promise them anything, to take care of his schooling first. Yet, he is also proud of Biff that girls "pay for you." This type of ambiguous message is typical of Willy's parenting. He contradicts himself often.
His next memory involves Willy's coming home from a business trip. Here he ignores Happy and focuses only on Biff. We see the effects of Happy being ignored when we look closely at the shallow, immoral adult Happy has become. He also praises Biff for stealing a football for practice. He calls this "initiative." Biff later is fired for stealing from Oliver; and when he goes to Oliver to ask for a stake in a business he and Happy are trying to start, Biff leaves with a stolen pen from Oliver's desk. Later we learn that Biff has been in prison.
Additionally, Willy disparages Bernard who attempts to tutor Biff in math as someone who is not "well liked." He tells Biff and Happy that they are built like Adonises and that the "man who makes an appearance in the business world . . .is the man who gets ahead." We later see that Biff is the one who failed math, never got his high school degree, never went on to college and that Bernard is the one who became a successful lawyer arguing cases in front of the Supreme Court.
Other mistakes involve Willy as a provider and a husband. In the following flashback with Linda, we see that Willy never really was a successful salesman, never really making enough to make ends meet, that Willy's colleagues laugh at him, that he talks too much, and that he is overweight. He is not the successful business man that he leads his sons to believe that he is. This reminiscence is interrupted with sounds of a woman's laughter. We later learn that this laughter is that of a woman with whom Willy is having an affair. Biff's discovery of this affair is what led to Biff's alienation from his father and his leaving home without a high school degree.
Willy thinks his biggest mistake was not going with his brother Ben to Alaska, a proposition that Willy believes would have made him rich. But this was not truly a mistake. Willy's true mistake was not being a better father to his sons or a better husband to his wife. Willy's mistake is that he did not face the reality that he was not a financial success and that Biff was not perfect.
I believe that you might be referring to perhaps Willy's biggest mistake and it was his refusal to go with Bernard to enter the timber business and instead following David Singleman's "get rich quick plan" as a salesman. Being that this would have made all the difference in Willy's life, his only escape at this point is to turn back in time and remind himself of Biff's big football game, which was also a pivotal moment in Biff's life. In both occasions, both men respectively lost their chance at success. If Biff had passed Math, he would have been able to go to U of VA and would have been a famous footballer. If his Dad had taken Bernard's plan, he would have been rich and successful.