What do we learn about the differences between the reality of Willy's life and the facade that he presents in Death of a Salesman?
This is an interesting question because it depends on the context in which you are asking it. Willie's "facade" isn't really a facade at all. Dictionary.com defines facade as "a front or outer appearance, esp a deceptive one" There is a sense of intentionality here and I think that is absent in Willie.
Instead, I think the problem is self-knowledge. When I think of Willie, I recall the words of "To a Louse" by Robert Burns:
O wad some Pow'r the giftie gie us
To see oursels as others see us
It wad frae monie a blunder free us
Of all knowledge, self-knowledge is perhaps the most difficult to achieve. Doestovesky, in Notes From the Underground" makes a interesting a relevant observation:
"Every man has some reminiscences which he would not tell to everyone, but only to his friends. He has others which he would not reveal even to his friends, but only to himself, and that in secret. But finally there are still others which a man is even afraid to tell himself, and every decent man has a considerable number of such things stored away."
The tragedy in "Death of a Salesman" isn't that he puts up a facade, but that "he had all the wrong dreams." He though that, in the world of business, relationship meant something, promises meant something ... that he meant something. He learned, sadly, that man is a piece of fruit --- you can, and we do, "eat the fruit and throw away the peel."
In Death of a Salesman, readers learn that Willy's life is very different in reality from the facade that he puts up in front of others. Willy says that he wants to be a great salesman and to be remembered for all his hard work. But Howard does not want to keep Willy as a salesman and he tries to tell Willy that he is not effective in his position. Willy tries to get Howard to believe that he was and is a great salesman and that he only needs a better opportunity to be successful. However, Howard knows the truth--that Willy is not as accomplished as he would like to believe. Howard knows that Willy does not possess the skills and talent to be a great salesman even if Willy will not accept this reality.