The circumstances of the Coronavirus disease caused by the SARS-CoV-2 virus (COVID-19) pandemic have had a significant impact on global and national developments, affecting the existence of society in all its expressions, as well as the lives of people themselves. In the context of the pandemic, increased attention has been focused on acute measures, but the ending of the pandemic is expected as a resolution of the related healthcare problems. However, there are several indicators that the COVID-19 pandemic might induce long-term consequences for individual and public health. Some of the consequences are inferred and predictable, but there are also areas of medicine that have been indirectly affected by the pandemic, and these consequences have not yet been sufficiently explored. This study is focused on drawing attention to some of the COVID-19 pandemic consistencies and the pandemic-revealed inconsistencies in healthcare. Content analysis and statistical analysis were applied to achieve the aim of the study. The main findings of the study address chronic disease burden (particularly, myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS)), healthcare governance and organizational issues, and the synergy between health policy perspectives and innovative solutions in practice. The study provides insight into the particular healthcare issues affected by the COVID-19 pandemic, such as the increase in mortality in some diagnoses besides COVID-19 and the possible emergence of a new type of resistance—vaccine-resistance—contemporaneously supporting the identification of the tendencies and currently unnoticed indirect consistencies and inconsistencies revealed by the pandemic.