Here's a link to the Register's editorial on the Supreme Court's Medellin v. Texas decision. It was a complicated case but a fairly simple principle, that only Congress (and state legislatures) can make law in the U.S. Medellin, a U.S. resident since age 3, is a Mexican national, and according to a treaty should have been entitled to see a consular official from Mexico. The issue wasn't raised by his defense until they were appealing the death sentence. The Supremes said the treaty wasn't self-executing -- it would have required Congress to pass a law to make it a new right in the U.S. So the state of Texas didn't have to grant a rehearing.
In fact, this case was taken to the World Court as a way of trying to weaken the death penalty in the U.S. and establish the power of the World Court to dictate domestic law in the U.S. There was no allegation that the trial on the crime, a brutal gang rape and murder of two teenage girls, was defective, or that consulting with a consul would have changed the outcome. I have no love for the death penalty; I'm suspicious of letting the State have that kind of power. But if it's to be changed in the U.S. it should be done by us, not stealthily through some international elite. organization.