Evaluation of construct validity, though usually far short of accurate prediction , often detects this type of problem. There is in general no simple relation between the precision with which measurements can, have, and should be done, and the accuracy of the theory used to understand those measurements. In the Social Sciences, the precision of measurements is generally far higher than the accuracy of theory. In Physics, vice-versa. I think it can be argued that many of the profoundest experimental discoveries are made when there is no theoretical guidance available about what to expect.
Physics looks for simplicity in the midst of every-increasing complexity.
Social Science in contrast is preoccupied with rejecting simplicity and looking for complexity, perhaps to disguise its lack of useful theory. There has over time been a systematic increase in the precision of the estimates and a systematic tendency to underestimate errors. Of course the situation has been much worse for some results that do not qualify as precision measurements. Perhaps the main lesson to be learned is that we should be somewhat skeptical of the precise values and their associated errors, but that we can rely on the prospect that future experiments, by physicists who are dedicated to pushing the envelope of what can be measured, will surely produce values of considerably greater precision. On knowing things better and better.