At work, in a garage, its common to see old batteries causing all manner of issues with warning lights etc. The battery can start the car fine but a failing cell within the battery can cause havoc.
Its most common with BMWs, even going back to Y reg (2001). It seems BMW electrics need a stable and reliable constant voltage to work correctly - this may well be the case other makes too. I have seen it on Jaguars too (Ford era) so not surprised at Johns findings.
Nothing beats a good scanner to go in at look in detail at all the values - sensor voltages/fuel trims and the like when looking for faults.
