I think it can be dangerous to underplay the vaccine reactions and side effects too much - it can even play into the hands of the antivax "why is no one admitting this" mob.
It's particularly the case with the Moderna jab, where is clinical trial data showed around 10% having adverse reactions - of the kind that might keep you off work the next day. Not life threatening in themselves, but scary if it comes out of the blue, and it'll be important that people understand when a "normal" adverse response becomes a dangerous one.
The immediate severe allergic reaction responses are low - but much higher than the equivalent flu jab. Again, they've all been handled quickly by the healthcare teams monitoring the patients, but not something to be too blase about. Particularly for people with a history of allergic responses, even if they hadn't previously reacted to a vaccine.
We're also seeing early data from places like Norway, where they're concerned about what happens to some of the oldest, most vulnerable patients. Crudely though, that's almost entirely a statistical exercise that has to be carried out. Comparing the actual deaths to expected deaths in their age/vulnerability group. Sadly there are going to be people for whom the next illness/fever/bout of inflammation or upset stomach will be their last, and for a tiny number them the vaccine may be that last straw. Just as covid would have been had they caught that.