As an illustration, around 2200 years ago, 200 years before Jesus, a Greek scientist actually measured the curvature of Earth not moving from his town(!) only by observing the shadow of the Sun and cleverly thinking, giving the circumference as "50 times distance between Alexandria and Siena." He didn't have the exact distance then, but knowing that distance today, he measured the circumference of the Earth with the error of less than 0.2%.
150 years later, still before Jesus, another scientist, Posidonius, repeated the experiment.
Most of the things we confirmed today survived a lot of checks. As Asimov writes it's not that there's much "wrong" in what science knows today, it just that is "incomplete" in the smaller (from the perspective of the common experience) details.
The difference to me is that "incomplete" means you are missing something: more precise measurements, better calculations, more information. But that is not necessarily the case. You may be able to measure the size of the Earth relatively precisely, but if your theory puts that Earth at the center of the universe, more measurements are going to do little but cause you headaches.
Take the ever-popular conflict between relativity and quantum mechanics. For all intensive purposes [sic], I believe they both work out to about Newtonian mechanics at scales I can easily observe and they both work very well for their different appropriate tasks. But they don't mesh well together, which is another requirement for science. "Incomplete" doesn't begin to describe that situation because I suspect that whatever is going to unify both is going to be as different from either as they are from classical physics.
[As an aside, I've seen Asimov's essay before and while I usually don't have a problem with his writing, in this essay's case I can't get past the fact that it is either very poorly written (if I'm feeling charitable) or a rather silly ad hominem (if I'm not).]
My example is totally orthogonal to the subject of the position of the Earth in the universe, I don't understand what can benefit from bringing the confusion in the discussion.
Your other argument is what scientists are well aware of for decades, so it's a good example of the science knowing its current limits, which again means we can't be wrong if we know the exact limits. We have unmapped terrains that span only first 1eā32 part of the first second! Can you even imagine how small that time is? There were 1e49 such time intervals since then! What's that when not a small "incompleteness" of our knowledge. That people who work on that call it "a big thing to unify" doesn't change the fact that it's something small to the vastness of the time we already cover with the present equations.
http://chem.tufts.edu/answersinscience/relativityofwrong.htm