Final answer:
The complaining party sends a 'writ of certiorari' to the higher court to challenge a trial judge's mistakes, with the United States Supreme Court being one such higher court that can issue such an order.
Step-by-step explanation:
The term for a written statement of the mistakes made by the trial judge, sent by the complaining party to the higher court, is often referred to as an appeal or an appellate brief. However, when specifically addressing the United States Supreme Court, this can also be known as a writ of certiorari(often abbreviated as cert). This is an order by the Supreme Court to review the decision of a lower court. The party that lost at the lower court level and is seeking review is the petitioner, and the case is titled with their name first, such as in Roe v. Wade or Brown v. Board of Education. A famous example of someone acting as his own counsel and petitioning for this review is Clarence Gideon, whose case led to all defendants having the right to an attorney.