It's different depending on which vaccine technology was used.
Some vaccines used a lipid shell to get around the problems of raw MRNA being really fragile. However, it seems they made the protection too good, and MRNA that was supposed to just stay in the arm easily travelled further and got into the bloodstream. That means that MRNA was getting into cells all around the body and causing spike protein production everywhere, instead of just in the arm like designed.
This means that you got inflammation problems everywhere in the body, including in the heart (myocarditis/pericarditis), vascular systems ("brain fog", general unwellness), and reproductive systems (especially for women).
Inflammation in the injection site for a vaccine is pretty normal, inflammation elsewhere is terrible.
Initial optimistic assumptions of the MRNA being permanently consumed by the body relatively quickly also don't seem to be true - even the CDC recently edited a page on MRNA vaxxes to remove a statement that the MRNA is used up quickly. The very worst case scenario could be people who got vaxxed just have cells pumping out inflammatory spike protein at a low rate for years.
Other vaccines used a real virus vector that is modified version to express spike protein. This of course has the issue of a virus being not entirely controllable once it's in the body. Again, you'll have the problem of the virus (and thus the spike protein it expresses) ending up in strange places. However, the immune profile is slightly different, as the immune system will start to attack the vaccine vector as it progresses in the body.
Several vaccines were associated with strange, systemic blood clotting in some people - but I'm not sure if they ever found the mechanism of action.
Novavax uses a traditional protein+adjuvant mix seen in many previous vaxxes. There's no widespread report of nasty side effects with Novavax - but there's not that much usage of Novavax in the wild either.
Aside from that, there's also the issue that in targeting a variant of the rapidly-mutating spike protein, you set people up to be victim to the long-known "original antigenic sin" effect.
Immune system works off a principle of first impression - it targets a response to whatever it sees first. This also applies to infections that are somewhat close but not the same as what is 'memorised' by the immune system already. So an infection by a COVID variant when the person has been exposed to a vaccine for the originals will produce an immune response for the modified original protein, not the real infection that is currently happening. (The vaccines target a modified original spike protein, and not the S-shape protein as well, so the distance is even greater.)
Since the spike protein keeps shifting so fast in the wild, hitting the OAS effect is really likely over time.
Some people think the S-protein in the middle of COVID should have been targeted by the vaccines, not the spikes, as it's more stable. It's hard to know if that would have been more effective.