I have a paper soon to appear in American Journal of Epidemiology on this topic, but today I gave a talk on this topic for a group of Epidemiology students and faculty at University of Pennsylvania today.
The talk covers various epidemiological fallacies that have led to people misinterpreting/misrepresenting observational data throughout the pandemic, with a focus on evaluating vaccine effectiveness and a short discussion on safety.
I also discuss a few of the key principles that need to be followed when analyzing observational data to avoid these fallacies.
Here is a video file containing the talk: