Short abstract:

One error in physics in the early 20th century persisted 15 years through work by 3 Nobel Prize winners and was eventually corrected by a graduate student. This case and other long-standing errors and "error cascades" help indicate when and how errors are corrected.

Long abstract:

Well, that’s how long it took to correct the error. By a graduate student, no less. Who had to fix something his advisor had received a Nobel Prize for. Along with errors in the work of two other Nobel Prize winners. All compounded, one upon another, with no one correcting the fundamental error -- an erroneous value for the viscosity of air. This tale of compounded error shows just how science failed to self-correct -- neither peer review nor replication (regarded conventionally as the stopgaps) caught the error. Correction did occur, ultimately?, stemming from conflicting results and substantial additional work tracking the source of the discrepancy. In general, error correction occurs when an incongruence --observational discordance, anomaly, or interpretive disagreement or ambiguity-- leads to further experimental work that probes alternatives and compares one case against another until some factor can be attributed to be ultimately responsible for an errant result, and thence remedied. > Allchin, D. 2015. Correcting the 'self-correcting' mythos of science. Filosofia e História da Biologia, 10, 19–35.