The other being that this new vaccine is developed so quickly that there hasn't been time to check for long term effects (in the order of years). Most existing vaccines took years to develop, and this allowed time for testing of long term effects.
I understand this second type of concern - the authorities need to put in some assurance about it, and re-ignite trust from those who are now very skeptical of the gov't and institutions. This skepticism can escape to other aspects of society - like trust in the election results, and other gov't institutions' neutrality and public good status. It is a crack in the system, which if not fixed quickly, could lead to the dam of democracy collapsing.
I take it you're the kind of person that runs alpha/beta software on production machines.