The new Coronavirus disease (COVID-19) has seriously affected the world. By the end of November 2020, the global number of new coronavirus cases had already exceeded 60 million and the number of deaths 1,410,378 according to information from the World Health Organization (WHO). To limit the spread of the disease, mandatory face-mask rules are now becoming common in public settings around the world. Additionally, many public service providers require customers to wear face-masks in accordance with predefined rules (e.g., covering both mouth and nose) when using public services. These developments inspired research into automatic (computer-vision-based) techniques for face-mask detection that can help monitor public behavior and contribute towards constraining the COVID-19 pandemic. Although existing research in this area resulted in efficient techniques for face-mask detection, these usually operate under the assumption that modern face detectors provide perfect detection performance (even for masked faces) and that the main goal of the techniques is to detect the presence of face-masks only. In this study, we revisit these common assumptions and explore the following research questions: (i) How well do existing face detectors perform with masked-face images? (ii) Is it possible to detect a proper (regulation-compliant) placement of facial masks? and iii) How useful are existing face-mask detection techniques for monitoring applications during the COVID-19 pandemic? To answer these and related questions we conduct a comprehensive experimental evaluation of several recent face detectors for their performance with masked-face images. Furthermore, we investigate the usefulness of multiple off-the-shelf deep-learning models for recognizing correct face-mask placement. Finally, we design a complete pipeline for recognizing whether face-masks are worn correctly or not and compare the performance of the pipeline with standard face-mask detection models from the literature. To facilitate the study, we compile a large dataset of facial images from the publicly available MAFA and Wider Face datasets and annotate it with compliant and non-compliant labels. The annotation dataset, called Face-Mask-Label Dataset (FMLD), is made publicly available to the research community.