Our society is built out of institutions. Schools, social services, the judiciary, governments… all of these are institutions. And where there are institutions, there is the possibility of corruption.
We attempt to deal with this by setting up independent watchdogs and having internal standards. The problem here is that watchdogs are reactive, not pro-active – they investigate complaints, but if the complaints are silenced before they reach them, they are impotent. They are reliant upon either whistleblowers, who are at risk of losing their job, having their career ended, and may even be blackmailed; or the corruption causing enough problems for someone with enough standing to get it brought to their attention. Internal standards, being part of the institution, suffer from the same rot that the rest of it does. If an organisation is thoroughly corrupt, it is incapable by definition of investigating itself. The action must come from outside.
Enter the Inquisition. Independent of those they investigate, answerable only to the top. There is precedent here in the form of the Chinese Censorate, officials tasked by the Emperor with making sure local government officials were doing the jobs they had been given. On a more fictional note, the Imperial Auditors of Barrayar, appointed directly by the Emperor himself, from the Vorkosagian Saga.
Inquisitors would not be bound by being given specific tasks. Their role would be more akin to a muckraking freelance journalist, who has been given a stipend to allow them to devote themselves full time to digging up whatever dirt exists wherever it exists. Though it is likely they would, as the Barrayar Imperial Auditors do, focus on the areas that have to do with their specific experience and competencies (I envisage inquisitors being recruited after they have already had a career, giving decades for them to be evaluated for trustworthiness and ability). A doctor would likely focus on the healthcare system, a judge on the judicial system.
The term Inquisitors conjures up unfortunate images of unaccountable power, executing and torturing citizens as they see fit. Our Inquisitors would not have, or need, such power. The only power they would require is unrestricted access. Their purpose is to observe and report, not to intervene. Should they find something they consider concerning, they write it up and submit it to the appropriate oversight body, likely a committee of the legislature (i.e. US inquisitors would answer directly to the Senate).
Nor would they require unrestricted access to everything. There are many reasons why a court hearing may be held behind locked doors, and someone appointed to audit family courts does not need clearance to sit in on matters of national security.
Could the Inquisitors themselves be corrupted? Certainly. Who watches the watchers is a question that has been asked for thousands of years. The answer (in addition to whichever body of government they answer to) is, as Samuel Vimes put it, “We all keep an eye on each other". If one is falsifying their reports, then that will be noticed when others investigating the same case start sending in theirs.
But let us consider for a moment what having an inquisition, perhaps Her Majesty’s Auditors, would mean. Could the grooming gang scandal have lasted as long as it did if there were people on the case who were not limited to the civilian powers of journalists, but could have observed the inner workings of the police, councils, and social services, and who could report directly to Parliament with their findings? Perhaps even then it would have been buried. But it would have taken only a single MP on the relevant select committee to speak up for it to be exhumed again.