COVID-19, caused by the novel SARS-CoV-2 virus, started in China in late 2019, and soon became a global pandemic. With the help of thousands of viral genome sequences that have been accumulating, it has become possible to track the evolution of the viral genome over time as it spread across the world. An important question that still needs to be answered is whether any of the common mutations affect the viral properties, and therefore the disease characteristics. Therefore, we sought to understand the effects of mutations in RNA-dependent RNA polymerase (RdRp), particularly the common 14408C>T mutation, on mutation rate and viral spread. By focusing on mutations in the slowly evolving M or E genes, we aimed to minimize the effects of selective pressure. Our results indicate that 14408C>T mutation increases the mutation rate, while the third-most common RdRp mutation, 15324C>T, has the opposite effect. It is possible that 14408C>T mutation may have contributed to the dominance of its co-mutations in Europe and elsewhere.