For your Turing machine example: even if we built such a machine, it would never truly be giving an answer to the halting problem, because any stray cosmic particle could excite the electron and cause it to cross whatever plane.

For a more realistic example: the ground state of an molecule is a physically relevant quantity, and in theory any molecule alone should lose energy and attain it's ground state, even if finding the ground state electronic configuration is undecidable. But in reality, no molecule is ever truly isolated and so would never actually be guaranteed to enter it's ground state (or if it were truly isolated, it would not be observed at all rendering the question moot)