In correctly predicting that selection efficiency is positively correlated with the effective population size (Ne), the nearly-neutral theory provides a coherent understanding of between-species variation in numerous genomic parameters, including heritable error (germline mutation) rates. Does the same theory also explain variation in phenotypic error rates and in abundance of error mitigation mechanisms? Translational read-through provides a model to investigate both issues as it is common, mostly non-adaptive, and has good proxy for rate (TAA being the least leaky stop codon) and potential error mitigation via "fail-safe" 3' additional stop codons (ASCs). Prior theory of translational read-through has suggested that when population sizes are high, weak selection for local mitigation can be effective thus predicting a positive correlation between ASC enrichment and Ne. Contra to prediction, we find that ASC enrichment is not correlated with Ne. ASC enrichment, while highly phylogenetically patchy, is, however, more common both in unicellular species and in genes expressed in unicellular modes in multicellular species. By contrast, Ne does positively correlate with TAA enrichment. These results imply that local phenotypic error rates, not local mitigation rates, are consistent with a drift barrier/nearly-neutral model.