If it caused cancer, or auto an autoimmune disease, its likely these wouldn't be apparent for months or years. This is unlikely, but possible, and we could not test for this thoroughly as we didn't have the time.
I also remind you that these companies are immune from lawsuits due to the indemnity clause in their contracts.
There have been some people who have been reinfected with it, but I saw another recent article about this latest research that talked a bit about those cases. It said that they are believe to be people who did not have a strong immune response the first time. The vaccines should produce a strong response.
[1] https://science.sciencemag.org/content/early/2020/10/27/scie...
[2] https://www.darkdaily.com/mount-sinai-researchers-find-that-...
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> Looking at this selfishly and from PoV of game theory, the best decision is to let vaccinate everybody else but don't take vaccine yourself. Obviously, not everybody can make same decision
There are two different ways a medicine might have long term unintended and currently unknown effects.
1. It does some kind of permanent damage to you fairly immediately after taking it that takes a long time to show noticeable effects, or
2. It does some some kind of damage that is not permanent and won't lead to any long term noticeable effects as long as the original damage is allowed to heal or at least not made worse.
Category two is what you have to worry about with things you have to take regularly, because they can accumulate the damage or risk and it can take many years before it accumulates to the point that we might notice.
Because this is a not a "take every year" kind of vaccine, I don't think there is much need to worry about category two.
With "take it once" types of medicine (yes, I know some vaccines require more than one dose over a week or two, which counts as taking it once when considering long term effects), with wide deployment, I'd expect any unintended and unknown long term side effects to start being found within maybe a year of wide deployment.