Disinformation, i.e., information that is both false and means harm, thrives in social media. Most often, it is used for political purposes, e.g., to influence elections or simply to cause distrust in society. It can also target medical issues, most notably the use of vaccines. With the emergence of the COVID-19 pandemic, the political and the medical aspects merged as disinformation got elevated to a whole new level to become the first global infodemic. Fighting this infodemic is now ranked second on the list of the most important focus areas of the World Health Organization, with dangers ranging from promoting fake cures, rumors, and conspiracy theories to spreading xenophobia and panic. The fight requires solving a number of problems such as identifying tweets containing claims, determining their check-worthiness and factuality, and their potential to do harm as well as the nature of that harm, to mention just a few. These are challenging problems, and some of them have been studied previously, but typically in isolation. Here, we design, annotate, and release to the research community a new dataset for fine-grained disinformation analysis that (i) focuses on COVID-19, (ii) combines the perspectives and the interests of journalists, fact-checkers, social media platforms, policy makers, and society as a whole, and (iii) covers both English and Arabic.