As I see it:
The main (and largely overlooked) point is that regulators issued Emergency Use orders for all the vaccines; none of them have gone through the years-long testing procedures which would normally be needed.
Issues got flagged; the regulators would likely suspend the use order until data on the issue had been reviewed. They have now issued revised regulatory advice with advice by age, just as many drugs say "don't mix with this other drug". As a professional on the BBC has just said, it's "safe but not risk-free" - the regulatory advice will continue to be revised.
This was always going to be likely - it's a learning process, and all the regulatory people will have been looking out for these things.