Although requiring prior knowledge makes the ideal binary mask an impractical algorithm, substantial increases in measured intelligibility make it a desirable benchmark. While this benchmark has been studied extensively, many questions remain about the factors that influence the intelligibility of binary-masked speech with non-ideal masks. To date, researchers have used primarily uniformly random, uncorrelated mask errors and independently presented error types (i.e., false positives and negatives) to characterize the influence of estimation errors on intelligibility. However, practical estimation algorithms produce masks that contain errors of both types and with non-trivial amounts of structure. This paper introduces an investigation framework for binary masks and presents listener studies that use this framework to illustrate how interactions between error types and structure affect intelligibility. First, this study demonstrates that clustering (i.e., a form of structure) of mask errors reduces intelligibility. Furthermore, while previous research has suggested that false positives are more detrimental to intelligibility than false negatives, this study indicates that false negatives can be equally detrimental to intelligibility when they contain structure or when both error types are present. Finally, this study shows that listeners tolerate fewer mask errors when both types of errors are present, especially when the errors contain structure.