Let's talk about the US's vaccine adverse event reporting system (VAERS), with emphasis on its misuse by bad actors.

VAERS is a self-explanatory system. I mean that literally: it tells you exactly how to use it (and how not to).

VAERS is a spontaneous (passive) reporting system. Anyone can submit a VAERS report, and certain events for certain vaccines are required to be reported by healthcare providers under the NCVIA law. Herein however lies one of the limitations.

https://www.cdc.gov/vaccinesafety/ensuringsafety/history/index.html

As an adverse event is anything bad that happens following the receipt of a pharmaceutical, it need not be causally related to the vaccine. If you look hard enough you can find VAERS reports for things that are obviously unrelated. For instance:

You can verify that these events are as they say they are because IDs are included to confirm them.
I hope we can all agree that "lyme disease," and "fart that left yellow stain in underwear 6 months post-vaccine" are not safety concerns pertaining to the vaccine.

Someone has even gone as far as to report that the vaccine turned them into the incredible hulk (however they were subsequently contacted and agreed to take the report down: https://www.politifact.com/factchecks/2017/may/11/bill-zedler/bill-zedler-insists-program-doesnt-collect-wide-ra/

In short, the existence of a VAERS report in isolation offers absolutely no evidence that the vaccine caused the stated harm in the report, or that it's even related at all.

You're going to see (or already are) screenshots of terrifying reports relating to COVID-19 vaccines.

This next point is very important: Anyone who goes diving into VAERS reports to claim a specific harm from the vaccine is either being dishonest or is unqualified to be opining on the subject matter. There is no assessment of causality attached to these reports.

VAERS reports have no controls to go with them, and they are invariably going to be biased accounts, most of which rely only on a temporal association.

As discussed here:
https://www.medpagetoday.com/special-reports/exclusives/90917

Rare things can happen rarely. It doesn't mean the vaccine is at fault.

A common claim among such disinformation artists is that only 1% or less of adverse events actually get reported to VAERS. This is misleading for several reasons, the first of which is: not everything needs to be.

We know that vaccines cause certain uncomfortable self-limiting effects (reactogenicity) and we don't need a VAERS report for every single one. They aren't safety issues that need to be addressed, which is the sort of thing we concern ourselves with in these systems.

Secondly, any time the vaccine is associated with any kind of serious medical issues, it's going to force people to seek care. We don't need passive reporting systems to capture these events. We have things like the VSD for that:
https://www.cdc.gov/vaccinesafety/ensuringsafety/monitoring/vsd/index.html

Indeed, VAERS is very much the tip of the iceberg when it comes to our vaccine pharmacovigilance:
https://www.cdc.gov/vaccinesafety/ensuringsafety/monitoring/index.html
https://www.cdc.gov/vaccinesafety/iso.html https://www.cdc.gov/coronavirus/2019-ncov/vaccines/safety.html

You might justifiably wonder then what the point of VAERS is given all these issues and the existence of all of these other systems. Mainly it's useful for hypothesis generation and It's fast. If you get a collection of a given adverse event, it's worth examining.

This is in fact how we learned that our first-generation rotavirus vaccines caused intussusception at a rare but still unacceptably high rate and led to their removal from market within a year of its introduction until safer vaccines were introduced.

https://pediatrics.aappublications.org/content/104/3/575.long

A team of professionals is constantly examining vaccine safety data for all vaccines, especially the COVID-19 vaccines. This was in fact a focal point of the last ACIP meeting:
https://www.cdc.gov/vaccines/acip/meetings/downloads/slides-2021-01/06-COVID-Shimabukuro.pdf

At this point, despite active soliciting of adverse events and follow up investigation regarding adverse events of special interest, there are no safety signals associated with the Pfizer or Moderna COVID-19 vaccines.

Surveillance of these vaccines will continue for as long as they are on the market and if they need to be withdrawn, they will be. If new events emerge that were missed in clinical studies and deemed related, patients will be apprised appropriately of the risks and benefits.