The challenges of breeding autotetraploid potato (Solanum tuberosum) have motivated the development of alternative breeding strategies. A common approach is to obtain uniparental dihaploids from a tetraploid of interest through pollination with S. tuberosum Andigenum Group (formerly S. phureja) cultivars. The mechanism underlying haploid formation of these crosses is unclear, and questions regarding the frequency of paternal DNA transmission remain. Previous reports have described aneuploid and euploid progeny that, in some cases, displayed genetic markers from the haploid inducer (HI). Here, we surveyed a population of 167 presumed dihaploids for large-scale structural variation that would underlie chromosomal addition from the HI, and for small-scale introgression of genetic markers. In 19 progeny, we detected 10 of the 12 possible trisomies and, in all cases, demonstrated the noninducer parent origin of the additional chromosome. Deep sequencing indicated that occasional, short-tract signals appearing to be of HI origin were better explained as technical artifacts. Leveraging recurring copy number variation patterns, we documented subchromosomal dosage variation indicating segregation of polymorphic maternal haplotypes. Collectively, 52% of the assayed chromosomal loci were classified as dosage variable. Our findings help elucidate the genomic consequences of potato haploid induction and suggest that most potato dihaploids will be free of residual pollinator DNA.