It's not a matter of appointment. This third branch of government simply said that they, too, have a place in determining what is constitutional law.
The legislature, when writing a bill, is cognizant of constitutional considerations, as is the President when he signs it. Both branches have a sworn duty to uphold the Constitution, and both branches may contest the constitutionality of a proposed piece of legislation.
The USSC only sees the legislation after it becomes law and is contested. One can say that they are the "final" arbiter, but that is only because they are the last signatory. Marbury v Madison established the USSC as one of the three branches making a constitutional determination.
Maybe that's your take on it, but what they said in Marbury is simply that they must follow the Constitution. That's virtually a direct quote. The holding was phrased not in terms of what the courts had the power to do, but in terms of what they lacked the power to do - namely, enforce unconstitutional laws.
The didn't claim that the meaning of the Constitution is to be determined by their rulings. They said that they must determine their rulings by the meaning of the Constitution.
I thought, "So at what point are we justified in concluding that a court opinion is wrong?" was a rhetorical question so I didn't bother to answer it. I have no idea when we're justified. I know when I am.
Actually it wasn't a rhetorical question, but that was a rather rhetorical objection to the question. So substitute "you" for "we" in the question, while considering the points I raised at #564.
Now that I think of it, before you do that, perhaps you can answer if there's ever any justification at all for concluding that a SCOTUS opinion is incorrect, even if the legislatve and executive branches haven't objected to it.