How might a court rectify a document when a mistake has occurred? Which of the following is correct?

Any mistake by any party allows for an application to court to rectify a document so that the mistake is fixed

Where the parties to an agreement draw up a document, which due to mistake does not appropriately reflect the actual agreement, then a court may rectify the document so that it appropriately reflects the agreement

Courts will, as part of their role in society, correct inappropriate written documents at the request of a mistaken party

Courts will re-write a contract where the parties are unable to agree on the original intentions between the parties due to a unilateral mistake