I wouldn't say there is a common fault which particularly afflicts MPi's any more than other Mini's. True enough the injection Mini's are less tolerant of low battery voltage as it causes the sensors to "tell lies" to the ECU, but that shouldn't be a problem once the alternator starts charging the battery back up again.
Check the usual suspects: main battery earth in the boot, battery terminals on both positive and negative in the boot, engine to body earth strap in the engine bay. Also on the injection models check the Brown coloured wires on the starter motor solenoid, they have a habit of getting green verdigris corrosion which can bridge out to the body of the starter, or cause the terminals to break up prematurely. Also check the master fuses are clean and the voltage at these master fuses is as close to battery voltage as possible. Sometimes the brown wires from the solenoid get micro-breaks in them which causes an increase in resistance, therefore loosing voltage and increasing demand on the battery and alternator.
Having said all of that, that would affect the car running rather than draining the battery.
The alarm and clock shouldn't draw a large quiescent current, nor should the radio, but you could check by disconnecting them and seeing if the battery holds up a while longer.
Finally if the battery has gone "dead flat" repeatedly then it's overall capacity will have diminished greatly and so it may be time to replace it. Personally I would say the 038 battery is on the small side for an MPi. There is a sticky thread on batterys in the main section here, many people recommend the battery from a Peugeot 306 diesel. I have one from an Astra/Nova Diesel which was installed in 2000, is only used for 6 months of the year if that, and is still going strong (there that's buggered it now !!)
Phil.