Homology is perhaps the most central concept of phylogenetic biology. Molecular systematists have traditionally paid due attention to the homology statements that are implied by their alignments of orthologous sequences, but some authors have suggested that manual gene-by-gene curation is not sustainable in the phylogenomics era. Here, we show that there are multiple ways to efficiently screen for and detect homology errors in phylogenomic data sets. Application of these screening approaches to two phylogenomic data sets, one for birds and another for mammals, shows that these data are replete with homology errors including alignments of different exons to each other, alignments of exons to introns, and alignments of paralogues to each other. The extent of these homology errors weakens the conclusions of studies based on these data sets. Despite advances in automated phylogenomic pipelines, we contend that much of the long, difficult, and sometimes tedious work of systematics is still required to guard against pervasive homology errors. This conclusion is underscored by recent studies that show that just a few outlier genes can impact phylogenetic results at short, tightly spaced internodes that are deep in the Tree of Life. The view that widespread DNA sequence alignment errors are not a major concern for rigorous systematic research is not tenable. If a primary goal of phylogenomics is to resolve the most challenging phylogenetic problems with the abundant data that are now available, researchers must employ effective procedures to screen for and correct homology errors prior to performing downstream phylogenetic analyses.