Re: sloppy wiring scenario
Er, when you say Bass pickup, do you mean a pickup in a bass guitar or are you using the expression - as PRS does - to mean neck/Rhythm position pickup?
As already mentioned above, reversing the two conductors on a passive pickup might affect the screening against RF interference and hum.
Electrical phase reversal can have an effect if you ever record overdubs to a recording begun before the wiring changes. Any time notes overlap, frequencies will cancel each other out, leading to a thin, weak tone.
If the pickup is a vintage-correct Fender design, the brass screening plate on its underside will act as an aerial. (Brace yourself for taxi radio issues à la Spïnal Tap!)
Probably best to put the wiring back the correct way around.