I wonder if resistive heating devices like ovens which have a tuned temperature component would become systematically less accurate if the frequency changed significantly.
Nah, the thermal time constant is a low-pass filter on the order of .01Hz, all of the line frequencies in this thread are waaaay higher than the control loop bandwidth. The loop would never notice the substitution.
You might be able to trip up a fancy soldering iron where loop bandwidth is intentionally maximized, but I still suspect the first thing to go would be the magnetics on anything with a transformer.
Yes, but not for the reason you'd think: 50 Hz magnetics have to be physically larger to work (peak flux density for a given current is higher), and magnetics are so big and heavy that they're not designed with much margin. So 60 Hz transformers will often not work at all at 50 Hz, and 50 Hz transformers will sometimes perform pretty badly at 60 Hz (though also sometimes going this direction works fine).
