It's not the argument you want me to make.<quoted text>
That is not the argument you want to make.
But what's that got to do with copying mistakes in DNA?Entropy in general has many interdisiplinary applications, statistical mechanics and information theory for example. Standard textbooks discuss this routinely. For example, Bromberg's Physical Chemistry, 2nd Ed. Or read the Wiki on Entropy, Boltzmann's Entropy Formula, etc.
The same amount of energy is used making an error as making a perfect copy. So there is no difference in entropy.
And natural selection (life) weeds out the dangerous mutations leaving only the harmless or beneficial.Each generation of each species is accumulating genetic mutations at the rate of approximately 100 - 300 new ones in humans. We all have them even if we don't show any particular disease. There are numerous recessive ones that is why it's not a good idea to marry your sister.