Common scab, calcium deficiency, and internal tuber defects, such as hollow heart, have severe negative impact on the marketable yield and profitability of potato (Solanum tuberosum L.) farmers. The present study was conducted to detect quantitative trait loci (QTL) controlling these traits. A tetraploid linkage map was constructed using 808 single nucleotide polymorphisms (SNPs) from the SolCAP 8300 Infinium Potato Array using 151 genotypes of an F1 population generated from a cross between cultivars with divergent traits, Atlantic and Superior. Atlantic is susceptible to scab and has high incidence of hollow heart and low tuber calcium. Conversely, Superior has resistance to scab, low incidence of hollow heart, and high tuber calcium. This population was phenotypically evaluated between 2009 and 2012. Seven QTL regions explained pitted scab incidence and severity; two on chromosomes 3 and 11 of Atlantic, and five on chromosomes 1, 2, 5, 6, and 10 of Superior were identified. Also, six QTL regions that explained tuber calcium variation were detected; four QTL were located on chromosomes 1, 4, 5, 7, and 8 of Atlantic; and one QTL on chromosome 3 of Superior. In addition, five QTL were identified for the incidence of hollow heart; two QTL were located on chromosomes 3 and 5 of Atlantic, and three QTL were located on chromosomes 3, 6, and 12 of Superior. These QTL regions can be further studied to develop markers for marker‐assisted selection.