Can mutation rate be selected for?
Yes.


  Evolutionary success of bacteria relies on the constant fine-tuning of
  their mutation rates, which optimizes their adaptability to constantly
  changing environmental conditions. When adaptation is limited by the
  mutation supply rate, under some conditions, natural selection favours
  increased mutation rates by acting on allelic variation of the genetic
  systems that control fidelity of DNA replication and repair. Mutator
  alleles are carried to high frequency through hitchhiking with the
  adaptive mutations they generate. However, when fitness gain no longer
  counterbalances the fitness loss due to continuous generation of
  deleterious mutations, natural selection favours reduction of mutation
  rates. Selection and counter-selection of high mutation rates depends
  on many factors: the number of mutations required for adaptation, the
  strength of mutator alleles, bacterial population size, competition
  with other strains, migration, and spatial and temporal environmental
  heterogeneity. Such modulations of mutation rates may also play a role
  in the evolution of antibiotic resistance.


https://www.ncbi.nlm.nih.gov/pubmed/16677295



Large differences in mutation rates can be found among viruses: 10^-3 mutations per nucleotide per replication in RNA bacteriophage Qβ versus 10^-8 mutations per nucleotide per replication in DNA Herpes simplex virus. Generally, RNA viruses have higher mutation rate because RNA-dependent RNA polymerases lack the proof-reading capacity present in DNA polymerases. However, both increasing and decreasing these typical mutation rates leads to reduced virulence of the virus population.

https://www.ncbi.nlm.nih.gov/pubmed/16220146

https://www.ncbi.nlm.nih.gov/pubmed/16327776