Since it is possible to code a restraint that is an incorrect assumption, we need to understand what the impact of that will be on our fit, with the hope that it can be detected. The key concept here is that if a restraint is realistic, then its inclusion in the fit will change the fit to the powder diffraction data only by very minor amounts (this is best noted by the \(\rm R_{wp}\) value for the powder pattern). It may have a large impact on the values of the restrained parameters, but as the weighting is reduced for the restraint, the \(\rm R_{wp}\) value should only change by perhaps 0.1 or less.
To understand this, as an example, let us consider a material composed of tetrahedral Al and Si atoms linked by O atoms. As was noted before, the expected bond distances for Al and Si are a bit different, 1.74 Å and 1.62 Å, respectively. Suppose that I make a mistake and label a site that actually contains an Al atom as having a Si atom and place restraints on the bond distances around that atom as 1.62 Å, even though the structure really has the longer Al-O distances. This incorrect model will have two inaccuracies. One is that there is an extra electron being placed on that site, but experience tells me that this will have negligible impact on the fit. The \(\rm U_{iso}\) will be enlarged a bit, but the \(\rm R_{wp}\)/GOF values will stay about the same. However, if the data have sufficient sensitivity to actually determine the bond distances for that site, the data and restraints will be in conflict. Without restraints, the bond distances would average about 1.74 Å, but restraints will push the values to be shorter. As the weighting of the restraints are lowered, the \(\rm R_{wp}\) value should drop as the fit moves away from the mistaken distances and towards the correct values. This may be be a subtle difference if the impact of the bond distances is very small. Also, if the restraint is needed because the model is insensitive to the bond distances, then one might expect the range of distances to become larger, but the average should stay close to the target, but if the target is wrong, then the average will change as the weighting is lowered. In truth, this mistake might be too subtle to find, but knowing what to look for at least makes it possible. With more egregious mistakes, the conflict between the data and the restraints would be more obvious.