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I've seen experiments verifying modeling with the Navier-Stokes equations, finite-strain elasticity equations, Cahn-Hilliard equations for phase decomposition, Laplace-Young for surface tension ... and yet I can't help but notice that all of those equations are continuum mechanics, whereas with other experiments we've become very confident that atoms are things which exist. Set up other experiments where a critical length is in Angstroms (or just one where the Knudsen number isn't negligible, for the Navier-Stokes case) and you'll get a result where the otherwise-well-verified continuum model fails. Perhaps "All models are wrong; some are useful" is too pessimistic to be true forever, but it's a good one for now, because the idea that we have a model which is never wrong is currently false.
And that's not just a matter of engineers being lazy about avoiding expensive atomistic models. Even in the most fundamental physics, there are no mathematical models currently in existence which do not fail verification in experiments outside their individual range of applicability. The goal of finding such a model, a "Theory of Everything", is naturally at the top of our list of unsolved problems in physics, but scroll down that list and you'll find our existing models failing to fit the bill because of a number of cases that are much worse than the continuum/atomistic divide. At least atomic models converge to cheaper continuum models in the limit.
F=ma isn't even true today, except in the special case where both are 0. It's a simplification of F=d(mv)/dt which neglects that inertial mass m is itself a function of velocity. You might say it's "mostly true" - our fastest spacecraft so far hit a speed a bit over 150 km/s, and at 0.0005c Newton is 99.99998% accurate - but the difference between "mostly true" and "relativistic effects are a thing" is where E=mc^2 came from. So at that point, I guess the question is, what would you count as "massively wrong"? If Newton got things 99.99998% right, but hidden in that 0.00002% was "there are rocks with a million times more energy than coal", does 0.00002 count as tiny or does 1000000 count as massive?
Our current theories seem to have gaps bigger than 0.00002. We've been unable to directly observe 95% of the mass-energy in the universe. Five times more than what we've observed is "dark matter", which we don't yet know the identity of but can indirectly observe via galaxy dynamics and gravitational lensing, and double that is "dark energy", which we can only infer by looking at the local shape and accelerating expansion of the universe. From a practical sense, perhaps none of that will turn out to be important - we discovered barely-interact-with-normal-matter neutrinos a lifetime ago and we haven't accomplished anything more than a little interesting astronomy with them, so the prospects for interacts-even-less-with-normal-matter technology don't look good to me - but from a theoretical sense, our best theories say there are gaping holes in our best theories! We are bound by the laws of physics, but we don't actually know what all the laws of physics are yet.
Yes, and I’d agree that in cases where what our experiments show breaks down that I don’t have a problem with putting a bookmark there and saying “we don’t yet understand this part” or something similar. If the data shows a problem as recognized by people working in that field, then sure, I’d trust them to understand the problem and what it implies and what kinds of solutions make sense in that particular breakdown point. On the other hand, breakdowns of specific theories in specific circumstances doesn’t issue us a blank check to put in whatever speculative ideas we particularly want to believe in. We know about relativity, even if we don’t understand it perfectly I think it safe to say we understand a lot of it. Our physics is good enough to be useful in 99% or more of ordinary interactions to fairly high degrees of accuracy. We’re talking about edge cases, and yes they’re important, but it seems like using edge cases to imply that we don’t know what the laws are, when we have a pretty good approximation of those laws, and they work well enough to predict the existence of phenomena long before we can detect them by simple observations. In fact we predicted the existence of black holes long before we ever saw one and we knew quite a bit about their behavior beforehand.
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