The evidence of Willy's lack of parenting skills is evident throughout the play, particularly when we witness that the lives of both sons of Willy Loman's, Biff and Happy, have turned out to be insipid and lacklustre, to say the least. 

Here are some of the most salient examples:

Ego and complaisance-

In Act I, we immediately see that Willy's parenting style is based on feeding his children's egos, and on being complaisant to everything and anything that they want to say or do. Bad call!

Willy chooses his own kids (of all people) to let them know how great they are. He instills in them a credo of superiority which would allow them to bully and abuse others. It is all fair game, according to Willy. After all, who asked the rest of the world to be born short, or bad in sports, or fat, or too nerdy? He tells his own children that they are build like gods, like "Adonises", and that they hold the key to success in that they are well-liked, and more popular than others.

Bernard can get the best marks in school, [...] but when he gets out in the business world[...] you are going to be five times ahead of him. That’s why I thank Almighty God you’re both built like Adonises. Because the man who makes an appearance [...] is the man who gets ahead. 

If this is not an example of the most pathetic parenting style out there, surely there is little to come right after. 

Enabling

When Willy sees his kids doing mischievous acts, he sees them as triumphs of youth, rather than indicators of behaviors that need to be controlled and modified right away. 

In scene 3, Act I, Willy remembers the time when Happy disclosed that Biff had stolen a football from his coach. While Willy immediately disapproves and tells Biff to return the ball, he gets mad at Happy (!) for telling on Biff. This is because Biff admitted that he stole the ball only so that he could practice for the Ebbets Field game and make a touchdown for his father. 

In this case, Willy praises Biff right after he scolds him. He claims that, in order to reach a goal, sometimes we have to justify the means to get there. Therefore, the theft of the ball was suddenly rewarded, making Biff appear more like a hero and less like a budding thief. Willy completely turned a good learning experience into an enabling one. Surely the confusion that came out of this change of heart is visible in Biff's adult life, where he second guesses himself about everything.

Yet, one of the most telling pieces of evidence of lax parenting is still seen in the present, when Happy and Biff invite Willy to dinner and, choosing to chase after two girls, leave their senile father behind.

It almost seems as if they knew that a quick "sorry" would suffice when they see their parents again, after the fact. This is true, especially when we see that Happy readily purchased flowers for his mother in an attempt to make up for what they did, which was pretty wrong. Therefore, the enabling, the complaisance, the ego feeding, and the contradictions that the Lomans were raised with are responsible for the type of irresponsible individuals that they are as as adults.