This is another very broad question. Short answer is, yes there are down sides to using a foam roller. Physician clearance is wise as things like vascular issues can be very serious.
The long answer literally fills books. I do teach instructors in the use of foam rollers, but it is not a simple “read this/do it” type of subject. One of the things that I feel can’t be taught properly via video or in a book. Having an experienced instructor teaching foam roller techniques is very important. I received instruction from physical therapists, surgeons, sports med physicians, etc. I would not be comfortable using foam rollers without that kind of knowledge.
Many people feel it is simple, but they are most likely not using foam rollers as effectively as they could. Or even in the best way for each client. Luckily, most people will have more than enough pain when using it improperly to stop them from doing much harm. But some will hurt themselves. An instructor who allows this to happen makes it harder for the rest of us to do our work.