I have never felt that the "anti-hero" category is all that helpful. There are so many definitions that it's difficult to know what we are talking about. I think I have a lot more sympathy for Willie than many readers; in fact I can see him as a modern tragic hero much as Miller wishes us to see him (I have a link to his essay below). Willie (would we see him differently if we didn't always refer to him by the diminutive form of his name?) makes a mistake, much like Macbeth does; he envisions success in all the wrong ways. Like Macbeth, who thinks that becoming King is the purpose of his life, Willie thinks that economic success will bring meaning to his life. They both start off as "noble," one with the nobility of position, the other with the nobility that belongs to all of us.
Sadly, it doesn't work out for either Macbeth or Willie; both make an initial decision that leads to their demise. Of course, once Macbeth makes his decision, there is no going back, and you could argue that Willie had "options" along the way. I do not think that this is the case; when you set out on a path that means everything to you, there may be no going back.
So I do not see Willie as an anti-hero; perhaps, as Miller sees him, he is the tragedy of man in a modern consumer society.
If you want to make the argument that WIlly is an anti-hero, you can start, as kwoo1213 said, by indicating that Willy does not possess any traditionally heroic characteristics, such a bravery, willing to take risks, putting others before himself, admiration of others, etc.
However, like a TRAGIC hero, Willy's pride causes his downfall--he is unwilling to accept help and admit his faults or mistakes, and therefore, he meets with a tragic death, though it is caused by himself.
Willy possess certain qualities that a lot of other anti-heroes have possessed--human weakness, disillusionment, lack of identity and lack of determination (in a lot of ways, WIlly can be seen as the lost Everyman of the 1950s).
Willy is not a "knight in shining armor" or a Superman, but he represents a lesson for those who come after him, and heros are usually seen a people who teach lessons to other and show them how to live.
I do have to agree with kwo01213 that Willy is not a hero in any sort of way (except maybe as a tragic hero), and his action are selfish. But if you need to make an argument that he is a hero or anti-hero, these are the points I would use.
Willy is not an anti-hero. An anti-hero is a character who does not exhibit the normal attributes of a hero and who people would not expect to be a hero, but who does something heroic in nature.
Willy obviously does not possess characteristics of a hero, so that part of the definition he meets; however, Willy does not do anything heroic in the play. In fact, he kills himself, which is his way out of the the miserable life he thinks he is living. I do not see Willy's suicide as a sacrifice to help his family. I see it as a desperate way out of his being a disappointment as a provider and because he was an adulterer. I consider his actions selfish and thoughtless in many ways.