The symptoms people are discussing don't sound particularly implausible to me. Active Noise Canceling works by destructive interference, usually by sampling input from a microphone and using DSP, which might involve a filterbank or fourier analysis to construct the antiphase signal. These systems are crafted around experimentally-derived models of average human auditory systems. However, there may be some non-zero percentage of people for whom the model might not be a perfect fit, at which point I imagine the results could be unpredictable. If I were to guess, one possibility is something like a low-level intermodulation that may interfere with the normal operation of the vestibular system.
The problem with the display may be related to user reports of some displays having issues with scan lines or interlacing. The flickering may be just on the edge of conscious perception but still enough that problems ensue. That one poster achieved relief with a replacement may support this hypothesis, since not all iPhones have this problem.