"While men are perishable things, justice will live as long as the human soul and the law will live as long as the human mind"

Justice and law are and always will be two separate things. Justice is the feeling we get when a law is carried out. The law is something that is intellectual while the justice has a sense of coming from the soul. There will always be a definite relationship to the two, however. When a law is carried out and enforced, we get a sense that justice was also carried out. The quote means that as long as man's thought is carried out there will be new, better and fairer laws and as long as the human soul survives there will be a sense of justice among the people. Also, if a law is enforced, there may not always be justice involved in it.
In Billy Budd, Billy is accused of murdering the master at arms. Budd is an extremely likable character on the ship and because of this the court's first reaction is to let him off completely without any consequences. The fact of the matter, however, was that Budd had killed a man. It didn't matter that he was such a nice guy and that he only did it because he couldn't find the words to express himself when the victim was lying straight to the captain's face. Budd still killed a man and because of this there had to be definite consequences. Unfortunately for Budd, the consequence for killing someone onboard was death by hanging, something that the entire crew was against and didn't agree with. While the law is carried out, nobody feels that it is justified to kill Budd for what he did.
In Inherit the Wind, Bertram Cates is accused of teaching evolution when it is illegal in an extremely religious town. As he continued to fight for the right to teach different ideas the entire town turned their backs on him. The ruling came down that Cates had in fact broken the law, however his consequence was extremely leniant. Many thought the sentence was far to lenient for what Cates did, but Cates and his lawyer, Drummond, thought differently. They decided to appeal to the ruling because they felt it was unjustified. This is another example that while the law may be carried out just as it was intended, it may not be justified.
Howard Zinn feels that if we as a people feel the laws we are forced to abide by we have a right to change these laws. We have an obligation to make sure every action the government and our courts take are justified. We have a right to be treated fairly and equally to all other people in terms of freedoms and prosperity.