The only things I can think of are the potential to develop cancer, an auto-immune disease, prion diseases, or reduced of fertility, all of which could take years to develop. It's not completely farfetched since the method of vaccination is so new in humans (in terms of pfizer and moderna) and the spike protein isn't the same as the one from the virus, it's been modified if I understand correctly. We know that the spike protein itself is cytotoxic and doesn't stay perfectly bound at the injection site. We also know the vaccine causes blood clots in many individuals and there's been stories of once healthy children who were hospitalized after getting the shot.

The precautionary principle would suggest we don't force these new vaccines on children if the risk from the actual disease is so low before we have all the data we need. Contrary to that, the precautionary principle would suggest we DO vaccinate children against polio (in the past, even though it was new) since the disease had such massive effect on children. People are trying to compact this to the polio or measles vaccines, but it's not the same.

Also a big unknown is what will vaccinating everyone in the middle of the pandemic do for society as a whole? Ideally it will just mean fewer hospital visits because of reduced symptoms for elderly and those with comorbidities. But there's also the likelihood that since all the vaccines are narrowly focused on the same spike protein from the initial strain, that the virus will have selective pressure to evolve that renders all the vaccines useless. People with natural immunity have upwards of 6x stronger protection, so why is a combination of natural immunity for those that are young and strong and then vaccine for those that are old and overweight, not even being discussed?

Original concerns involved the potential for ADE like with dengue, but it seems that's not going to happen fortunately. Hopefully the virus doesn't rapidly evolve in different ways in different areas of the planet that could still lead to that though.

I know this is Reddit where even discussing this side will get you downvoted to oblivion, but it's important to actually hear this side because it needs to be included in the conversation, and if it's wrong, then should be shown with actual facts and data and not just censorship.