What sort of assay could be used to identify mutants with mutator phenotype?
There are a number of ways to screen for mutator genes. One straightforward approach in bacteria is to take an antibiotic sensitive non-mutator strain, grow it up, and expose to different antibiotics. Cells that survive in the presence of multiple antibiotics have acquired multiple de novo resistance mutations and thus are highly enriched for mutator alleles. Here is one example: Wiegand et al (2008) AAC.