Why is it important that both copies of the dna molecule have the exact same sequence of nucleotides as the original dna molecule?

The real problem is that t he mutation can lead to further problems in the future, if a cell divides and DNA duplicates again. So if they don't have the exact same sequence of nucleotides then the structure is not going to be accurate and that could lead to problems to the future growth. For example, in humans the consequences can lead to malformations.