Are the tips of the twisted red & white wires from the pickups soldered togther (it's hard to tell in the photos)? If not, for each pickup (separately) they need to be soldered and should then be insulated with some tape.
The two volume pots should have their 'non-wire' lug linked to ground via the back of the pot. Just solder a short link of bare wire from the lug to the back of the pot. You need this for the volume controls to work properly.
And, it's always hard to tell with those long flush-mount jacks, but you may need to swap the red and black wires on the lugs. If it buzzes when you touch a pot it usually means your jack's hot lug is actually connected to your guitar's ground and vice versa.