I think one of the biggest themes that this play points towards is the recognition of a different code of laws in separate communities that often stands in conflict with the national law. Miller presents us with a world that is full of Italian immigrants, and thus the community operates under a mix of Sicilian and American laws. This "code" is characterised by the protection of illegal immigrants, the importance of family and hard work and the shipping culture and, most importantly for the play, the sacredness of trust and the desire for revenge when a member of the community has been wronged.
Clearly, however, when Eddie Carbone chooses to prevent the marriage between Catherine and Rodolpho, he points out the massive conflict between this "code" and the American system of justice. By appealing to American state law, Eddie Carbone forsakes his own respect and identity which is incredibly important to him. Note how the small community is shown as being victorious compared to American law in the way that the community avenges its own member who has now turned against it. In spite of Alfieri's pleas to Marco that "only God makes justice," Marco, on behalf of the community, makes his own justice by killing Eddie for his betrayal of his community.
I'm interested in this question too, but how does Miller show us that Eddiemis complex? And how does he evolve troughout the play?