Human Induced Pluripotent Stem Cells (hiPSC) are an established patient-specific model system where opportunities are emerging for cell-based therapies. We compared and contrasted hiPSCs derived from different tissues in the same individual and across two large hiPSC cell repositories. We show extensive single-nucleotide mutagenesis in all hiPSC lines, although fibroblast-derived hiPSCs (F-hiPSCs) are particularly heavily mutagenized by ultraviolet (UV)-related damage. We analysed genome sequencing data on 454 F-hiPSCs, 101 blood-derived hiPSCs (B-hiPSCs) and 141 B-hiPSC derived subclones, as well as transcriptional data on 78 B-hiPSCs to gain further insights. Across 324 whole genome sequenced (WGS) F-hiPSCs derived by the Human Induced Pluripotent Stem Cell Initiative (HipSci), UV-related damage is present in ~72% of cell lines, sometimes resulting in substantial mutagenesis (range 0.25-15 per Mb). Furthermore, we find remarkable genomic heterogeneity between independent F-hiPSC clones derived during the same round of reprogramming, due to oligoclonal populations within fibroblasts. B-hiPSCs showed lower levels of genome-wide mutations (range 0.28-1.4 per Mb), no UV damage, but a strikingly high prevalence of acquired BCOR mutations in ~25% of lines. Genome-wide selection analysis revealed strong selection pressure for BCOR mutations in F-iPSCs and B-iPSCs. Directed differentiation experiments and RNA sequencing showed that BCOR mutations have functional consequences in affected B-hiPSCs. All hiPSCs had otherwise stable, diploid genomes on karyotypic pre-screening. Our work strongly suggests detailed nucleotide-resolution characterization is required prior to using hiPSCs for disease modelling or clinical applications.