You're absolutely right. The likelihood that any particular amino acid-generating codon will mutate to another amino acid-generating codon is non-uniform and the analysis of what impact these particular redundancies has on that is very complex - sometimes, certain amino acids can even stand in for each other.

Certain mutations from one acid to another are more desirable than others, so it's quite possible that the existing structure biases the amino acids towards certain least harmful mutation tendencies.

The whole thing is pretty fascinating.