I have just recently assembled, calibrated, and test-played my OpenTheremin V3. With what little I know, I believe the instrument to be performing as expected. It sounds reasonable to my ears.
Furthermore, according to the lone entry about grounding in the FAQ, I don't seem to have a grounding issue:
Q: The volume antenna does not seem to work
Make sure the theremin is grounded well. This can be a reason for the volume antenna not working well. See the instructions for different grounding methods.
There is a chassis ground on the OpenTheremin V3 that I have yet to connect. It is recommended in the assembly instructions to ground the power, audio, and/or the chassis.
OpenTheremin V3 - Circuit Board PCB:
My power (USB -> 120v AC) is NOT grounded, and I'm using a fairly typical 3.5mm to speaker system, which I believe has some grounding in the cable sleeve only.

Do I need to chassis-ground my Theremin?
What should I be experiencing without the ground, and what should I experience with the ground?
Here is a quick video testing my Volume Antenna on the latest V3.1 firmware with my current chassis-ground which is a twisted-copper speaker wire tied tightly around the ground cutout, and grounded to an exposed metal pivot on my tripod. To me, the volume antenna seems a bit non-linear, but I also have the volume pot turned all the way to the right to get better line-out volume on my computer.