Why not do make the function that outputs answers also feed itself "is this actually right/are you sure/is this not wrong"? Too expensive? Giant loop?
It can't tell it's wrong, it just reacts in a plausible well to you telling it it's wrong (acknowledging it and giving another explanation). Since ChatGPT is an expansion of GPT-3, those things won't be really solved since being somewhat of a knowledge base is a nice side effect, not the main goal of the model.
So you are saying the order of events if:
1. you ask it a question
2. it gives you an answer (in this case, it's wrong)
3. you ask it "are you sure? i think that's wrong"
4. it answers again "you are right, i think the answer i just gave you was wrong, here is what i think is the right answer this time" (and again, it's wrong)
and repeat forever?
They do this, with humans. Both during training (they use supervised and reinforcement learning), and now at a much greater scale: it's what the free public access period is for and why there's a thumbs up/down button next to the output.
Then you reset your session, you ask the same question and you get the wrong answer again.