Inferring aspects of the population histories of species using coalescent analyses of non-coding nuclear DNA has grown in popularity. These inferences, such as divergence, gene flow, and changes in population size, assume that genetic data reflect simple population histories and neutral evolutionary processes. However, violating model assumptions can result in a poor fit between empirical data and the models. We sampled 22 nuclear intron sequences from at least 19 different chromosomes (a genomic transect) to test for deviations from selective neutrality in the gadwall (Anas strepera), a Holarctic duck. Nucleotide diversity among these loci varied by nearly two orders of magnitude (from 0.0004 to 0.029), and this heterogeneity could not be explained by differences in substitution rates. Using two different coalescent methods to infer models of population history and then simulating neutral genetic diversity under these models, we found that the among-locus heterogeneity in nucleotide diversity was significantly higher than expected for these simple models. Defining more complex models of population history demonstrated that a pre-divergence bottleneck was also unlikely to explain this heterogeneity. However, both selection and interspecific hybridization could account for the heterogeneity observed among loci. Regardless of the cause of the deviation, our results illustrate that violating key assumptions of coalescent models can mislead inferences of population history.