Long-read sequencing technologies have revolutionized genome assembly producing near-complete chromosome assemblies for numerous organisms, which are invaluable to research in many fields. However, regions with complex repetitive structure continue to represent a challenge for genome assembly algorithms, particularly in areas with high heterozygosity. Robust and comprehensive solutions for the assessment of assembly accuracy and completeness in these regions do not exist. In this study we focus on the assembly of biomedically important antibody-encoding immunoglobulin (IG) loci, which are characterized by complex duplications and repeat structures. High-quality full-length assemblies for these loci are critical for resolving haplotype-level annotations of IG genes, without which, functional and evolutionary studies of antibody immunity across vertebrates are not tractable. To address these challenges, we developed a pipeline, "CloseRead", that generates multiple assembly verification metrics for analysis and visualization. These metrics expand upon those of existing quality assessment tools and specifically target complex and highly heterozygous regions. Using CloseRead, we systematically assessed the accuracy and completeness of IG loci in publicly available assemblies of 74 vertebrate species, identifying problematic regions. We also demonstrated that inspecting assembly graphs for problematic regions can both identify the root cause of assembly errors and illuminate solutions for improving erroneous assemblies. For a subset of species, we were able to correct assembly errors through targeted reassembly. Together, our analysis demonstrated the utility of assembly assessment in improving the completeness and accuracy of IG loci across species.