What about long-term effects we don't know about yet?
Here is what the checked sources say. Each title links to the original.
Feature Article: Long-term Side Effects of COVID-19 Vaccine? What We Know.
CHOP's article (February 2021, updated March 2022) reviews serious side effects vaccines have actually caused, including paralysis from oral polio vaccine, Guillain-Barré after the 1976 swine flu vaccine, narcolepsy after one 2009 flu vaccine, and low platelets after MMR. It says the onset of these effects was within about eight weeks of vaccination, and that the rare COVID-19 vaccine problems found later (myocarditis, clotting, GBS) also began within days to weeks. CHOP adds that science does not allow anyone to say long-term effects can never happen.
Incidence of narcolepsy after H1N1 influenza and vaccinations: Systematic review and meta-analysis
A well-documented example of a serious harm linked to a vaccine: narcolepsy, a sleep disorder, after Pandemrix, a 2009 H1N1 flu vaccine used in Europe. In this review the risk appeared limited to that one vaccine. In the first year after vaccination, risk rose 5 to 14-fold in children and teens (about 1 extra case per 18,400 doses) and 2 to 7-fold in adults. Finnish and Swedish data suggested risk extending into the second year, which the authors say needs caution because of possible bias; all the studies are observational.
The Childhood Immunization Schedule and Safety: Stakeholder Concerns, Scientific Evidence, and Future Studies
A 2013 Institute of Medicine committee report, which calls itself the most comprehensive examination of the US childhood immunization schedule to date, reviewed the evidence on the schedule as a whole, under which children could receive up to 24 immunizations by age two. The committee said it uncovered no evidence of major safety concerns associated with following the schedule, and it set out how to study the schedule further using existing or new data systems if safety signals arise.