Final answer:
The claim is false; errors during DNA replication can be corrected by proofreading mechanisms and post-replication mismatch repair. Unfixed errors can cause permanent damage and possibly lead to cancer.
Step-by-step explanation:
The statement that 'Errors in nucleotide sequencing that occur during replication cannot be corrected' is false. The process of DNA replication is designed to minimize errors through a proofreading mechanism where DNA polymerase identifies and corrects a wrongly inserted nucleotide. Furthermore, post-replication mismatch repair mechanisms can identify and replace incorrectly paired bases that have been missed by the proofreading function of DNA polymerase. Mutations in the mismatch repair mechanisms can result in errors that lead to more severe and permanent damage to the DNA sequence, which could result in conditions such as cancer.