Strong harmonics which overpower the fundamental will fool a zero-cross analysis, resulting in, say, a double or triple frequency output if the 2nd or 3rd harmonic is strongest. The strongest signal present will overwhelm the amplitude sign of the combined signal; so it still works even in the presence of some noise or other signal.
High amplitude noise will also skew results resulting in a higher frequency output. Low-pass or band-pass filter can work wonders.
Again, zero-cross analysis is suitable for simple use cases where you are directly sampling a signal.
I wonder if you could take just the sign changes of the input signal and use that in lieu of the zero crossings and get something useful out of it, for instance, a finger print for chords or harmonics.
High amplitude noise will also skew results resulting in a higher frequency output. Low-pass or band-pass filter can work wonders.
Again, zero-cross analysis is suitable for simple use cases where you are directly sampling a signal.