What is this about some idiosyncratic effect the proposed Covid vaccine is supposed to have on our DNA?

This doesn't exactly answer your question and i'm no scientist but one thing i feel confident about is that there won't be just one vaccine that will go to everyone on the planet. Instead, there is a multitude of them which have been developed using different types of methods and will work in various ways - ie come at the problem from different directions, so groups of people will get certain ones. It's a fast tracked process the likes of which we have never seen, but i have confidence that we will be ok long-term.