Accurate facial expression analysis is an essential step in various clinical applications that involve physical and mental health assessments of older adults (e.g. diagnosis of pain or depression). Although remarkable progress has been achieved toward developing robust facial landmark detection methods, state-of-the-art methods still face many challenges when encountering uncontrolled environments, different ranges of facial expressions, and different demographics of the population. A recent study has revealed that the health status of individuals can also affect the performance of facial landmark detection methods on front views of faces. In this work, we investigate this matter in a much greater context using seven facial landmark detection methods. We perform our evaluation not only on frontal faces but also on profile faces and in various regions of the face. Our results shed light on limitations of the existing methods and challenges of applying these methods in clinical settings by indicating: 1) a significant difference between the performance of state-of-the-art when tested on the profile or frontal faces of individuals with vs. without dementia; 2) insights on the existing bias for all regions of the face; and 3) the presence of this bias despite re-training/fine-tuning with various configurations of six datasets.