Formal auditing strikes me as a completely unhelpful layer of bureaucracy.
What is needed is a culture of sharing code and data (unless that is impossible due to restrictions on the data that was used), and the tools to allow this to happen.
This is already happening, we just need more of the same.
One issue is the incentive structure in many fields means that you only get rewarded for both collecting data, and analyzing it. Therefore there is a big incentive not to share data, since you get little or no credit when someone else uses your data.
While I have a lot of sympathy for the idea of improving the "quality" of science, I think the risk is that highly subjective standard could be used as a tool to suppress newcomers. Sometimes, "old-school", cruder experiments are perfectly fine, especially if the experimenters address the possibility of complicating factors - sometimes you just can't afford to buy toys that will get you from 95% confident to 99% confident, in the eyes of reviewers, and some subfields are incredibly closed and territorial (meaning collaboration with people who do have those toys is impossible).
Ideally, the solution would be, ok, just get your results out there and make the materials publically available so anyone who wants to take your solution to a higher standard can do that freely, but if you are prevented from communicating your result, then it never gets even that shot.
What is needed is a culture of sharing code and data (unless that is impossible due to restrictions on the data that was used), and the tools to allow this to happen.
This is already happening, we just need more of the same.
One issue is the incentive structure in many fields means that you only get rewarded for both collecting data, and analyzing it. Therefore there is a big incentive not to share data, since you get little or no credit when someone else uses your data.