Now I have had a chance to get used to the player mustang, there are a couple of issues/niggles with the electronics. Nothing major but enough that I'm going to attempt to fix them.
First, when switching to the jazz/bridge pickup soloed, sometimes this results in no sound whatsoever. The neck pickup and middle position are fine. After considering whether to replace the switch with a blend pot or another switch, I decided that I'd prefer a better switch, so I have ordered a short switchcraft one. I'm thinking that it might have been better to order a right-andled switchcraft, but I'll see how the short one is when it arrives. Cleaning or messing about with the existing switch wasn't an option as in my experience any fix will only be temporary.
The second issue seems to be a widespread issue with the player mustangs due to how they are wired. When the volume is at any position other than full, turning down the tone results in a big loss of volume. The best explanation for this I have been able to find is that these basses use a 50s style of wiring where the volume control is wired back to front, and the fix for this is to swap around the two wires at the volume pot: 1. from the output of the switch, and 2. to the tip of the output socket. I will try this mod, and replace the switch when the new one arrives, and report back on whether this fixes the issue.
Factory wiring:
Proposed modification - desolder the two wires marked red at the volume pot and swap their positions: