DNA replication is a process that involves copying the DNA molecule. If a single base was miscopied, what would be a possible result of this for the cell in which it happened?
ll the proteins the cell creates from the miscopied strand will do different jobs than the old ones.
If the new sequence codes for the same amino acid as the original cell, it will function normally.
Both new DNA strands will end up together in a new cell, and the inaccurate one will be discarded.
Any miscopied DNA will be replaced with an accurate DNA copy once the cell divides.

If a single base is miscopied during replication then there is a possibility that the new base which has been incorporated will specify the same amino acid just like the old base. It happens because genetic code is degenerate which means that more than one codon can specify same amino acid. There are mainly 20 amino acids but codons are 64. In such scenario a few amino acids are specified by more than one codon.

For example: Leucine, serine and argenine are specified by 6 different codons.

Let us take example of leucine which is specified by codons CUU, CUC, CUA, CUG etc. If DNA is being copied and 'C nitrogenous base' of CUC codon is accidentally miscopied to 'nitrogenous base G' resulting into CUG codon instead of CUC. But still the type of protein which will be produced by this DNA sequence will be the same because it does not matter whether the DNA sequence has CUC codon or CUG codon the resulting polypeptide/protein will have leucine as amino acid.