We evaluate an annotation schema for labeling logical fallacy types, originally developed for a crowd-sourcing annotation paradigm, now using an annotation paradigm of two trained linguist annotators. We apply the schema to a variety of different genres of text relating to the COVID-19 pandemic. Our linguist (as opposed to crowd-sourced) annotation of logical fallacies allows us to evaluate whether the annotation schema category labels are sufficiently clear and non-overlapping for both manual and, later, system assignment. We report inter-annotator agreement results over two annotation phases as well as a preliminary assessment of the corpus for training and testing a machine learning algorithm (Pattern-Exploiting Training) for fallacy detection and recognition. The agreement results and system performance underscore the challenging nature of this annotation task and suggest that the annotation schema and paradigm must be iteratively evaluated and refined in order to arrive at a set of annotation labels that can be reproduced by human annotators and, in turn, provide reliable training data for automatic detection and recognition systems.