re: Wiring -
You'll need to de-solder pretty much everything and start over. You have the wire colours and connections mixed up.

The BLACK wire is the signal wire (hot) which is to be soldered to the input lug of the pot, not the back.

The GREEN & BARE wires are your ground, and DO get soldered to the back of the pots.

The RED &WHITE wires should not be connected to the pots (unless you're trying to slit the coils, but that would still be incorrect the way it is now). When you unsolder the red & white wires, keep them soldered together but insulate them with heat shrink tubing or electrical tape so they don't short across the shielding tape.

I think the cap is connected properly, but hard to see completely.
Your BLUE bridge ground wire is fine.
Also the interconnecting ground wires (GRAY) are ok too.

Here is the PBG TB-4 Diagram
The diagram only shows 2 wires from each pickup, so just pretend the RED & WHITE aren't there and GREEN/BARE = 1 wire (ground) and BLACK = the second wire (hot).


As for you earlier post about the bridge and string action, I'm unclear on what exactly the issue is if the height adjust posts are able to go down further.