Well perhaps you could actually prove the correctness of coq itself.
In any case it's just a matter of reliability in the traditional sense: we're going to end with a small set of statements that will have to be verified by humans upon which we can rest everything else. Those statements will need enough people looking at them to get a level of certainty we're comfortable with.
I believe the risk of a major flaw going unnoticed is astronomically low, and the good thing is this certainty propagates all the way to modern proofs if we take care to go through formal verification.
In any case it's just a matter of reliability in the traditional sense: we're going to end with a small set of statements that will have to be verified by humans upon which we can rest everything else. Those statements will need enough people looking at them to get a level of certainty we're comfortable with.
I believe the risk of a major flaw going unnoticed is astronomically low, and the good thing is this certainty propagates all the way to modern proofs if we take care to go through formal verification.