How does the US Court System rectify itself when a preceding case was incorrectly decided?

A court can overturn a decision by one of its inferior courts, or a decision by that court itself. They can ignore decisions that come from courts not in their jurisdiction; the First Circuit is not bound by Second Circuit precedent, and a Maine state court does not have to follow a Connecticut state court's interpretation of Constitution. (Sometimes which court is superior depends on what is being argued. Maine courts must follow federal courts` interpretations of federal law or the Constitution - but the federal court must follow the Maine state courts` interpretation of state law or the state Constitution.)

The doctrine of "stare decisis" says that they should not overturn precedent on a whim. Imagine the chaos if, every time we got a new member of the Supreme Court, all previous decisions were redone. Nobody could have any confidence in what the law is. Even if you knew how the current court would rule on your case, by the time your case went through all the appeals and reached the Supreme Court a justice might retire and be replaced and they could rule the other way.

But they do sometimes overturn a previous decision. One of the most famous examples is Brown v. Board of Education, which overturned Plessy v. Ferguson.

Define a "wrong" decision. One you don't agree with?

They can reverse the original decision.

There is an Appeals process.

A person who came out on the wrong end of a verdict can appeal to a higher court, but they need to prove the first court did something wrong. Applied a law improperly, didn't provide them their full rights, some sort of improper procedure, etc. If the appeals court agrees the first court did something wrong, they will reverse the ruling.

There are usually several stages of appeal that one can try for, ultimately being the Supreme Court of that state or the Supreme Court of the USA if it was tried in a federal court.

This is so rare, we can study individual cases.