The concerns about the magnetic field may be bunk, but I had to give up using a wireless charger next to my bed because I could hear the coils making a ticking sound. Qi interleaves data with power so I assume the sound is the coils reacting mechanically whenever they interrupt the power to send a data packet instead.

I found that some USB wall chargers emit a high pitched whine when used to power a Qi charger as well, even if they are dead silent when charging a device directly.

Being able to hear the coil whine and finding it annoying is a fine reason to not like wireless charging. But I am pretty sure this is not what most people are going on about.

Is the ticking a function of a mechanical relay in a cheaper device, or the coil not being sufficiently glued down and moving as the magnetic field is turned off and on?

The sound comes from the windings within the copper coils vibrating due to Hall effect in the alternating magnetic field. Yes, the physical construction of the coil matters as to how much it would whine; tighter and more regular windings and appropriate potting/adhesives counteract the physical effects. The easiest mitigation, however, is to just use a switching frequency much higher than humans can hear. AFAIK the Qi standard supports the charger using anything from 80-300kHz and can vary depending on what the charger decides is optimum. Any audible coil whine from Qi would be attributable to harmonic mixing within the physical system of the vibrating coil. Also note that the coil whine could come from either the Tx or Rx coil, so you might easily eliminate it with a different charger that settles on a different frequency or has a better manufactured coil. But if the problem coil is the one in your phone, you might be hosed!

The latter I think, I found the volume varied depending on how the coils were aligned. I'll give it another shot once Qi2 brings Magsafe-like perfect alignment to non-Apple devices.