"Why didn't they discover the new number was higher right away? It's a thing that scientists are ashamed of—this history—because it's apparent that people did things like this: When they got a number that was too high above Millikan's, they thought something must be wrong—and they would look for and find a reason why something might be wrong. When they got a number close to Millikan's value they didn't look so hard. And so they eliminated the numbers that were too far off, and did other things like that..."
While wrong by a statistically significant amount, Millikan's initial value was still much less than 1% off. It's really not a good example of the scientific consensus being completely wrong, because there was no consensus until Millikan's number had been shown to be wrong.
https://en.wikipedia.org/wiki/Oil_drop_experiment