In reality many boundary disputes turn on the precise locations of physical features and their correlations with the descriptions of the land parcel of the relevant conveyance, including the plan. This is actually a question of applying the descriptions of the land parcel to the physical facts on the ground at the time of the conveyance.
Where two or more of the descriptions conflict, the Court must make up its mind which of them is to prevail. Once the choice has been made, the Court may then apply the doctrine of falsa demonstration non nocet (a false description does not harm) to the other descriptions.
Hunter J in Lintock v Attorney General  HCA 5820/1982 said:
“In those circumstances it seems to me impossible to extract the parties’ intention with any sort of clarity from the four corners of this document. I have got to go outside it. I have got to look at all the surrounding circumstances. But this is a process of construction, not rectification. …..” (Emphasis added)
Parties occasionally enter into a contract on the basis of a common assumption which they later discover that there was mistake. Mistake is an extremely difficult area of the Contract Law. Legal terms such as “unilateral mistake” (單方面的錯誤), “mutual mistake” (相互錯誤), “common mistake” (共同錯誤),“mistake negativing consent” (否定同意的錯誤), “mistake nullifying consent” (使同意無效的錯誤), “misrepresentation” (失實陳述), “fraudulent” (欺詐性), “negligent” (疏忽性), “innocent” (無意性), “frustration” (受挫), “remedy” (補救), “damage” (損害賠償) are too difficult to understand. I am afraid that I do not have the knowledge to discuss the terms here.
Once the contract has been interpreted, one of the parties may argue that the written agreement, as interpreted, fails to reflect the agreement which the parties actually reached. In such case the Court may be asked to rectify the document so that it accurately reflects the agreement which the parties did reach.
Rectification is a remedy which is concerned with defects not in the making, but in the recording, of the contract. Rectification is an equitable discretionary remedy.
A Court will only rectify a document where ‘convincing proof’ is provided that the document fails to record the intention of both parties, unless one party knows the other is mistaken. The document must have been preceded by concluded contract or by a ‘continuing common intention’.
Regarding land boundary disputes, I have not found any English Court case on rectification of land boundaries. Furthermore, there is no English Court case on a mistake as to the identity of the subject-matter of the contract, i.e. both parties thought that they were dealing with one thing when in fact they were dealing with another.