I think that I've wired things wrongly - was I supposed to wire all the leads going to ground to the volume pot?
You should have the red wire going to the left-hand tag on the pot, the green and white soldered together and the black - plus the bare wire - soldered to ground (i.e. the back of the pot).
The middle tag of the pot should go to the "hot" tag of the jack, and the right-hand tag of the pot should also be grounded to the back of the pot.
There should also be two more ground wires soldered to the pot, from the bridge/spring claw and from the jack.