I have a plethora of problems with my R53. Searching the forum didn't yield anything similar enough to my situation. Hopefully someone can help narrow this down.

1. While driving, usually 5-10 minutes after starting up, the battery light will illuminate and stay on for another 5-10 minutes. It will then become intermittent and either flicker for a while or simply go out. I have experimented and cannot find any relationship between the light and driving factors such as wheel speed, engine RPM, bumps in the road, or electrical load. Note also that I have the MINI accessory gauges installed, and the voltmeter indicates a consistent 13.5-14.5V at all times. I have also stopped by an Autozone and had them test the battery & alternator with their little briefcase-sized device, and both tested out fine, including when under high load.

2. After shutting down the car, about one out of every five times, some strange things occur: the dash lights blink randomly, the JCW shift light does its startup cycle, the gauge needles flick to and fro, and occasionally the taillights & 3rd brakelight remain illuminated. I can generally make this go away after cycling the ignition switch a few times, but I have no idea what the car is doing while I am away.

3. The system is throwing a code (CEL illuminated), but I don't have access to a code reader at the moment.

4. [Addendum] I tried to start up the car today and it is 100% dead. No remote unlock, no dome light, nothing. So I suppose I will have to tow it somewhere and get that code looked at after all. I was hoping to do some troubleshooting on my own before paying to be raped by an NYC mechanic.

My guesses as to what might be the problem include:

a. Dying battery or bad cell. 5 years ago the battery went bad and some odd things occurred with the power locks and windows that suggest the dashboard pinball machine may be a similar problem. And the timeframe is about right for a failing battery. But the consistent voltmeter data would seem to contradict this possibility.

b. Bad alternator and/or voltage regulator, possibly overcharging while running and remaining energized when the car is off.

c. Bad body control module. Anyone want to buy a MINI?

 

I would start with the battery first. Check first to see if the clamps on the terminals are tight. I have read where some people have had several problems due to a bad battery or bad connection. Our dome light would not dim to nothing after start up and I would have to reach up and shut it off manually.
My solution was that I found that one of the battery clamps was not clamped tight on the terminal. I tried tightening it and man does that break easy. Tried calling a Mini dealer to see how much it would cost to replace the clamp and all they wanted to sell me was the entire cable for $65. I went to a VW dealer and got the clamp for $11. After that the dome light worked as it should.
We have an R50 so your battery clamps are probably different since yours is in the boot.

 

I checked the battery cables, and they seem firmly fixed. That was a bit of a challenge, because the back of the car was full of heavy items from work, and without electricity I have no access through the hatch. No recourse to the manual hatch release either, because (if I have one) it's trapped under the rear seat delete platform :(

 

Update:

It turns out the culprit was a defective power steering pump that had been installed the day before these problems began. The pump would remain active at all times, including while the car was turned off. Apparently this is a known, but uncommon, mode of failure. Replacing the pump has resulted in the problems going away (so far).

This is particularly frustrating because I was reluctant to fix the broken pump the first time, having gotten used to driving without power steering. Now I am going to engineer my own power steering delete as soon as I can cheaply source a used steering rack to tinker with.

 

Ps pump runon is pretty common failure mode, espically when a rebuilt pump is uded (uses used electronics, since no new is avalable). Too bad you did not hear the pump humming after shutdown...would have made life simpler. Keep an eye on the battery now....once killed, they usually have a MUCH shorter life......