Take for example Lord Kelvin's model of thermal conduction in a solid Earth. He used it to incorrectly predict the age of the Earth, but if he had taken that failure to heart he could have used it to predict mantle convection and plate tectonics.
General relativity is more complex and quickly goes in complicated mathematical weeds but is just as profound from a philosophical point of view, which is that things do not merely affect other things around them, but instead change space-time itself. You can see with a couple of clicks observations of phenomena predicted by it, like black holes and gravitational lenses. It’s interesting to think about even if you are not directly affected.
That said, those effects would have been small, and likely handled in practice as "some arbitrary consistent (or random) error."