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So -- when errors started cropping up -- they didn't experience "doubt" but... . . . what? What's the right word for their feelings then?

Thomas Kuhn and The Structure of Scientific Revolutions spring immediately to mind on the question of anomalies and shifting paradigms. Kuhn seems especially relevant to this conversation generally, as well:
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A scientific community cannot practice its trade without some set of received beliefs.
I was in Peru when the first man walked on the moon, and I remember my amusement when the cook at my host's house dismissed the whole thing as a hoax. There's no small measure of condescension in our current view of the recalcitrant who rejected scientific evidence that the earth was not flat and that the sun does not revolve around us for so long.

In reality, that concept conflicts with the working knowledge we derive experientially in our ordinary lives, and which we are essentially asked to reject as false. The sun, and the shadows it casts, certainly appear to move across the ground. Even now, you'd have to have put away a lot of beers before you'd put your bottle down on a beach ball. We flatten out road maps to register them on paper and frankly, as an ordinary civilian, I take the edicts of the scientific priesthood more on faith than understanding. I certainly can't see most of what they tell me, and almost any educated person can tick off a liar of contemporary examples where they've proved themselves wrong. Back to Kuhn:
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A shift in professional commitments to shared assumptions takes place when an anomaly "subverts the existing tradition of scientific practice." These shifts are what Kuhn describes as scientific revolutions—"the tradition-shattering complements to the tradition-bound activity of normal science"

There are more things in heaven and earth.....