So, maybe it's not so much that we have stuff "figured out", as it is that we have mental models that, while they work well enough to make certain predictions, also constrain our thinking in terms of what phenomena are possible. The "EM drive" controversy is one example of this tension.
I'm not so sure of this. Have you heard of Edward Leedskalnin, or his "Perpetual Motion Holder"? The textbooks that I have discussing magnetism do not explain this effect, which you can see an example of here: https://www.youtube.com/watch?v=eWSAcMoxITw
If you can explain this effect with our "current theories", I would love to hear it!
There's another interesting effect where an electric charge can be pulled from that set-up. Lasersaber demonstrates that here: https://www.youtube.com/watch?v=S_ssUTRbRRs
I certainly can't explain it, and I don't think we have an adequate theory that does explain it (yet).
In other words, much of the problem we face in the current scientific age is due to the fact that our instruments are now electron microscopes and Hadron Colliders, instead of carefully made glass beads and simple mirrors.
It's similar to problem faced in software of managing increasing complexity. No silver bullets known of yet for all those problems, just chronic application of powerful minds to the problem. :)
For example within medicine when computer power and AI is advanced enough to help us much more connecting the dots between DNA, viruses, environment etc.