This is a subject of debate, as each person has a personal definition of what the "whole truth" is.
However, there are certain truths in the play Death of a Salesman, by Arthur Miller, that definitely do need to be confronted by the Loman family because that is the only way to break with their vicious cycle of make-believe and denial.
As far as what truths should be exposed, the first is the fact that Willy is no longer a successful salesman and that, perhaps, he was never one. Sadly for Willy, it is not that he does not know this, but that he does not accept it. So, in general, whether he is confronted with this truth or not, it may not make a difference.
Another truth that does come out, thankfully, is Biff's actual connection to Mr. Oliver. When he realizes that he has been following his father's steps in idealizing relationships with people, Biff takes the initiative to confront Willy with it. Again, Willy withdraws to his fantasy world, but Biff finally awakes to reality.
However, some truths may remain in the dark. Biff obviously never tells Linda about Willy's mistress, nor about the stockings. Perhaps this is for the best. What would Linda do differently without Willy in her life? It is obvious that Willy and Linda are each other's enablers and they feed off each other. Linda idealizes Willy and allows him to do as he pleases as the head of the household. This being said, it would have made Linda's life more miserable to know about Willy's infidelity, but it would change her life- only make it worse.
In that case, what she does not know will not hurt her. However, that is entirely a matter of opinion. Some people swear by telling the truth no matter how badly it hurts. Others feel that telling the entire truth about something will redeem them from "sin". Yet, in the opinion of others who look out for the interest of the innocent, sometimes truths will not change anything but attitudes. It is a matter of what is the truth, and who is telling it.