I don't think we will ever get the breakthrough you are looking for. Things like design patterns and abstractions are our attempt at this. Eventually you need to trust that however wrote the other code you have to deal with is sane. This assumption is false (and it might be you who is insane thinking they could/would make it work they way you think it does).
We will never get rid of the need for QA. Automated tests are great, I believe in them (Note that I didn't say unit tests or integration tests). Formal proofs appear great (I have never figured out how to prove my code), but as Knuth said "Beware of bugs in the above code; I have only proved it correct, not tried it". There are many ways code can be meet the spec and yet wrong because in the real world you rarely understand the problem well enough to write a correct spec in the first place. QA should understand the problem well enough to say "this isn't what I expected to happen."
We will never get rid of the need for QA. Automated tests are great, I believe in them (Note that I didn't say unit tests or integration tests). Formal proofs appear great (I have never figured out how to prove my code), but as Knuth said "Beware of bugs in the above code; I have only proved it correct, not tried it". There are many ways code can be meet the spec and yet wrong because in the real world you rarely understand the problem well enough to write a correct spec in the first place. QA should understand the problem well enough to say "this isn't what I expected to happen."