For the problem with the inner/outer coils at positions 2 & 4, I would just turn the neck pickup 180 degrees. The other issue with the one coil missing at position 3 sounds like there may be an unwanted connection/short between a couple of adjacent lugs on the outboard side of the switch.

EDIT: See photo attached--is that a solder bridge between the two adjacent lugs?

switch_solder_bridge.jpg