That happens even with a basic tetanus. ALL vaccines are risky, just as ALL surgeries are risky. Zheesh, just leaving the house for work every day is risky. Everyone has to weigh the risks on either side.
Another thought just occurred to me, too. Since so many people - worldwide - are getting vaccinated in a short period of time, we have a LOT of data on side effects. I'm not downplaying the risks of this particular vaccine (or of not getting it,) but I wonder if there is any way to legitimately compare the Covid vaccine to others that may be widely used/applied but don't have readily available immediate results to study. Sounds like another overly-expensive project ... but it sure would be interesting to see a valid comparison.