Genomics is narrowing uncertainty in the phylogenetic structure for many amniote groups. For one of the most diverse and species-rich groups, the squamate reptiles (lizards and snakes, amphisbaenians), an inverse correlation between the number of taxa and loci sampled still persists across all publications using DNA sequence data and reaching a consensus on the relationships among them has been highly problematic. Here, we use high-throughput sequence data from 289 samples covering 75 families of squamates to address phylogenetic affinities, estimate divergence times, and characterize residual topological uncertainty in the presence of genome scale data. Importantly, we address genomic support for the traditional taxonomic groupings Scleroglossa and Macrostomata using novel machine-learning techniques. We interrogate genes using various metrics inherent to these loci, including parsimony-informative sites, phylogenetic informativeness, length, gaps, number of substitutions, and site concordance to understand why certain loci fail to find previously well-supported molecular clades and how they fail to support species-tree estimates. We show that both incomplete lineage sorting and poor gene-tree estimation (due to a few undesirable gene properties, such as an insufficient number of parsimony informative sites), may account for most gene and species-tree discordance. We find overwhelming signal for Toxicofera, and also show that none of the loci included in this study supports Scleroglossa or Macrostomata. We comment on the origins and diversification of Squamata throughout the Mesozoic and underscore remaining uncertainties that persist in both deeper parts of the tree (e.g., relationships between Dibamia, Gekkota, and remaining squamates; and between the three toxiferan clades Iguania, Serpentes, and Anguiformes) and within specific clades (e.g., affinities among gekkotan, pleurodont iguanians, and colubroid families).