The Supreme Court
The Supreme Court settles the disputes in connection with the election of the vice president and the president . Its verdict is final.
Customs Court
As best as I can tell, the Supreme Court, which is a federal court, settles disputes between neighboring states.
The Supreme Court of India
Supreme Court
The election of the president.
It is the judicial branch, namely the Supreme Court, that has the ultimate responsibility of settling legal disputes in the United States. The court was established in Article III of the U.S. Constitution.
According to Article III, Section 2 of the Constitution, the US Supreme Court settles disputes between states.
Supposedly the United Nations.
The Judicial branch settles court cases (disputes between individuals). That is not their only job though. They also interpret how the law is to be upheld and carried out.
Mediator