Strikingly consistent correlations between rates of coding-sequence evolution and gene expression levels are apparent across taxa, but the biological causes behind the selective pressures on coding-sequence evolution remain controversial. Here, we demonstrate conserved patterns of simple covariation between sequence evolution, codon usage, and mRNA level in E. coli, yeast, worm, fly, mouse, and human that suggest that all observed trends stem largely from a unified underlying selective pressure. In metazoans, these trends are strongest in tissues composed of neurons, whose structure and lifetime confer extreme sensitivity to protein misfolding. We propose, and demonstrate using a molecular-level evolutionary simulation, that selection against toxicity of misfolded proteins generated by ribosome errors suffices to create all of the observed covariation. The mechanistic model of molecular evolution that emerges yields testable biochemical predictions, calls into question the use of nonsynonymous-to-synonymous substitution ratios (Ka/Ks) to detect functional selection, and suggests how mistranslation may contribute to neurodegenerative disease.