Some New Confucians and Neo-Reactionaries argue that this kind of basic oversight should be provided by a novel council/board of "wise scholars", or people with real intellectual accomplishments which are not under serious dispute-- appointed with very long, perhaps lifetime terms. There's really no equivalent to this in the U.S. other than perhaps the Supreme Court, but the House of Lords in the U.K. is quite similar and does not currently have much of a political role, so it could be repurposed with relative ease.

> How can a separation of powers approach still check itself?

If you approach the problem (and it is in fact a very real problem) from an engineering/computing perspective, would a possibly useful approach be to develop an AI that consumes all (or as much as possible) relevant data, and then spits out instances of events where accountability is lacking? Tune it on the overly eager side so it spits out lots of false positives along with legitimate issues, and then a bipartisan committee that consists of representatives from various factions (government, corporate, unions, finance, law enforcement & military), as well as the general public to sort through what comes out.

This would obviously be a fairly major undertaking, but nothing beyond all sorts of other things we do on a regular basis I wouldn't think, and from the amount of news stories and forum comments on the matter, I think the problem is big enough to spend a fair amount of time and money on coming up with some solution.

It's named "common decency" for a reason.

Nobody is going to teach their kids to unleash their bulldog when someone does not agree with you ;)