Anomaly detection in hyperspectral images has proven valuable in many applications, such as hazardous material and mine detection. The benchmark anomaly detector is the Reed-Xiaoli (RX) detector, which is based on the local multivariate normality of background. The RX algorithm, along with its many modified versions, has been widely explored, and the main concerns identified are related to local background covariance matrix estimation. The small sample size, local background nonhomogeneity, and the presence of target pixels within the estimation window are factors that can deeply affect local background covariance matrix estimation. These critical aspects may occur together in the same operational scenario, and they may strongly impair the detection performance. However, due to their intrinsic difference, these aspects have been typically discussed within different frameworks, disregarding the possible existing connections while developing different approaches to solution. We investigate these critical aspects, along with their impact on the detection process, from an operational detection perspective. The approaches to solution are critically analyzed, discussing possible links and connections. Real hyperspectral data are employed for assessing if the algorithms, designed ad hoc to solve a specific problem, can either handle more complex situations, or bring about further complications.