In the play, the central example of how justice and the law are not always the same is found in John Proctor. The law finds him guilty of witchcraft when we know that he did nothing of the kind. He is innocent of the charges and so is put to death. There is nothing just about killing an innocent person, even if it is the law which sentences that person to death.
Law and justice are especially intriguing concepts in this play because of its Puritan setting. Salem at the time was a theocracy--a system whereby man's laws are also God's laws. Law is the means of achieving; justice is the goal of a legal system. They are not mutually exclusive, as we see in other countries whose laws do anything but reflect justice.
Here's a modern life example: If an 18 year old breaks into my house in the middle of the night and, thinking my life to be in danger, I shoot him dead, it is considered a legal act of self defense. That is, the law says I can do so to protect myself. But did he receive justice? Does killing someone for breaking a window and entering someone else's house resemble a just application of law? I don't think so.
In the play, the Puritan court is most certainly the law, but the 19 people put to death certainly did not receive justice.
I think that the topic is driven by the idea that justice is seen as an idyll to which all social orders strive. The law is the vehicle that help deliver societies to the realm of justice. The challenge, as presented in Miller's work, is what happens if the vehicle is usurped by those who do not have the selfless aim of justice in mind. Instead, these individuals are "driving under the influence" of personal agenda and the consolidation of power. Indeed, in these situations justice and the law are very different, for the latter becomes subject to the whims of individuals. The previous post does a stellar job of pointing this out in terms of disproportionate sentencing for drug use and abuse. Miller is suggesting that if the law falls into the wrong hands, when there is no institutional checks against abuse of power, then justice is in fact denied, even if the legal system says it to be delivered. I would examine how the inauthenticity of the trials in Salem prove this.
I can't really help you with the play, but if you think about it, there are a lot of instances in modern times where you can see laws that are unjust. Take, for example, the fact that penalties for possession of crack cocaine are way higher than those for powder cocaine. Both drugs are destructive, but one is punished way more harshly than the other. So what's just about that?
Another example, not from the US, is the fact that the laws of Saudi Arabia do not allow women to drive. Is that just?
So the point that you can make is that laws tend to be made by people with power. What they see as good may not always seem good or just to most people.
I can't give you examples from the play, but I do know that Tituba, for example, is in a powerless position -- she's both non-white and a woman. The laws end up getting her, right?
Law can be bent while justice is a general universal concept. Laws strive to uphold justice, but justice is more of a concept and therefore it is also bent in this case in the play.