Genome-wide association studies (GWAS) have become a powerful tool for analyzing complex traits in crop plants. The current study evaluates the efficacy of various GWAS models and methods for elucidating population structure in potato. The presence of significant population structure can lead to detection of spurious marker-trait associations, as well as mask true ones. While appropriate statistical models are needed to detect true marker-trait associations, in most published potato GWAS, a 'one model fits all traits' approach has been adopted. We have examined various GWAS models on a large association panel comprising diverse tetraploid potato cultivars and breeding lines, genotyped with single nucleotide polymorphism (SNP) markers. Phenotypic data were generated for 20 quantitative traits assessed in different environments. Best Linear Unbiased Estimates (BLUEs) for these traits were obtained for use in assessing GWAS models. Goodness of fit of GWAS models, derived using different combinations of kinship and population structure for all traits, was evaluated using Quantile-Quantile (Q-Q) plots and genomic control inflation factors (ëGC). Kinship was found to play a major role in correcting population confounding effects and results advocate a 'trait-specific' fit of different GWAS models. A survey of genome-wide linkage disequilibrium (LD), one of the critical factors affecting GWAS, is also presented and our findings are compared to other recent studies in potato. The genetic material used here, and the outputs of this study represent a novel resource for genetic analysis in potato.