The Judge is directly linked to the Midas Mulligan mystery and mythology, and like many of the older members of the Atlantis community, he is a sort of living legend, more closely tied to the past than the corrupt present. Both Mulligan and the Judge quit over the same case: a lawsuit in which a loser demanded a loan from Mulligan. The Judge ruled against the loser, a Lee Hunsacker, who was tied to the infamous Twentieth Century Motor Factory, but his ruling was overturned by another, corrupt, judge. Narragansett joined Galt's strike shortly after this case, feeling he could no longer practice law in the real world.
The Judge is sort of the chief political figure in Atlantis, and it's fitting that his final scene shows him rewriting the constitution (pretty bold!). His addendum naturally has to do with rights for businesspeople:
He was now adding a new clause to its pages: "Congress shall make no law abridging the freedom of production and trade . . ." (18.104.22.168)
We're guessing the Judge must have added another clause to the Constitution saying that he has the power to rewrite it, since the Founding Fathers didn't exactly say that any dude with some White-Out could go to town on it. Like most of the Atlantis crowd, the Judge does want he wants!