In matters of faith, I expect a simple truth to be better than a sophisticated error. If so, we can draw some inferences on the patterns we should see if a church is in error.
If a church is careful but not infallible in its doctrine, we expect it to get basic matters right. If an error does creep in, it will be subtle and hard to spot, possibly embedded in a complicated detail of advanced theology. Lay members would only learn the basic doctrine and never hear the error. They would have the benefit of simple faith, while the priests and theologians would be the ones plagued by error. The subtler the error, the more advanced knowledge would be required to learn it.
If a church is careless, or flawed in its foundation, even basic doctrine could contain error. Then laity and clergy alike would suffer from it.
If we can identify the consequences of error, we can infer its location by looking at the pattern. If all suffer equally, even basic doctrine is in error. If only clergy suffer, the error is more subtle. If only the highest-ranking clergy suffer, the error is so subtle that most priests don’t learn it. The greater the variation within rank, the less central the error is to church teachings. If the laity suffer and the priests don’t, then the doctrine may be sound but it’s being taught in a misleading way.
This also suggests that unsupervised study of theology could be hazardous. If you take error as truth, or misunderstand a truth, you will be in error until corrected. For most, simple faith is the safer path.