Backstory
So, the Kingdom of Maliscyle used to have an inquisition, to weed out the cult of the horned lord (a terrible demon). But... they found they were almost as bad as the cultists, as they just started doing what inquisitors are now known for. So, the inquisition was purged, and the kingdom settled for a time of peace and prosperity.
...Until the demon cults started flaring up again, and they remembered why they had an inquisition in the first place.
So, the next king made a hard decision, and decided to organize the inquisition 2.0; now with less tortured confessions, guaranteed! ...But is it guaranteed?
Goal for the Inquisition
The inquisitorial organization has two branches. One is basically the police, who enforce religious laws, cracking down on demon cults.
The second branch is legislative and more ecclesiastical in nature. They decide what is and isn't heresy. In the past, this lead to them deciding whatever was convenient to them was heresy, and using the enforcement branch as hitmen.
Now, though, they still need someone to decide matters of the kingdom's religious laws (freedom of religion kind of exists in Maliscyle). They don't want the king or anyone else to do it, because they think it's too much power for other government institutions. Instead, they're hoping to let the ecclesiastical branch handle it, but this time with some sorts of checks and balances to prevent the runaway corruption of last time.
Proposed solution
The general idea they had, was that the legislative branch is made up of a large council (about 300 members). Most actions require a two thirds majority, and passing a harsh law requires a 90% majority to agree.
Their second idea for a check, was that if a large enough number of the nobility (including the king) disagree with the law, then it is annulled.
The details would be rather complex, but the general thing is that as little as 18.75% of the nobles, if the king supports them, can annul a decision; if they're properly concentrated into one demographic. If the voters are spread out, and the king does not support them, then it could take up to half the nobles, 50%, in order to annul a decree of heresy.
Police
The police branch would be put under the authority of the secular police. In effect, it'd be just another branch of law enforcement, similar to NARCs.
They also gave them the equivalent of an internal affairs division, to keep an eye on them. Finally, they removed a lot of their powers to torture for information, and reduced the credibility of unverifiable confessions of magical events, which were impossible to prove.
They hope this is enough to prevent the inquisition from assassinating people with false reports.
Outcome
The general idea for the story was that, surprisingly, it seems to be working out. The inquisitors are checked by the king and nobles, so most of their decisions are semi-democratically approved by the oligarchy, without giving the nobles or king direct control of church matters. The close scrutiny of the inquisitorial police reduces corruption, until the corrupt feel quite out of a job.
That's when the Horned Lord would spring his own plan into action, subverting their little dream society.
Question
So, to clarify, there are two elements to this question:
How can the Inquisition be reformed to do its job? I offered one proposal I thought was interesting, but I wanted to hear others, and hear opinions on that proposal.
As an optional additional point, how do you think the Horned Lord could exploit the system I suggested, or the one you suggest, in order to break down the society? Most societies have some weakpoint that can be exploited, so a demonic influence could whisper suggestions and corrupt certain officials, or could send his cultists to infiltrate offices or take advantage of loopholes.
In other words, I'd like you to describe a reform program for the inquisition, but to also point out the exploitable weak points of the system you present.