Alfieri is one of the strangest characters in all of Miller's works. He acts like a Greek chorus in the play, and his viewpoint is the "view from the bridge" between the US legal system and older, cultural or tribal 'law'. He is an Italian-American, a student of American law, but still loyal to old Italian customs. In more than one way, he's a combination of the old and the new.
Therefore his view of the interaction between American Carbone and his Italian relatives purports to be objective, and even-handed. The big question about him is whether it is or not: which provokes the same question about the potential bias of the play as a whole.
Alfieri breaks the fourth wall and talks directly to the audience. It seems he tells the story which the play re-presents: and he comments on the events and the characters regularly. He's actually quite inconsequential to the action of the play as a character, but hugely important as an alienating reminder to critically judge the characters and events we are watching. By ruining the illusion of reality, we, like Alfieri, powerlessly watch the events unfold, and try to understand what this modern fairy tale might show us.