Pfizer has starting releasing their vaccine safety data per a court-ordered instruction to satisfy a freedom of information request. The data for the first 3 months has been released and partially analyzed.
Due to the push to vaccinate seniors, who are most vulnerable not just to Covid but to a wide variety of illnesses, the generally special vulnerability of Americans due to specific co-mobidities, the unprecedented scale of tracking, and the sheer numbers of people vaccinated, the rate of adverse reactions is on the high side of vaccines, though still within range of vaccines cited for comparison. It's worth noting that these were the earliest phases of vaccinations, with the oldest patients, and may not reflect later & better managed outcomes.