I have a 02 Mini Base.
We have replaced the alternator and the battery. Voltage at the battery shows that it is indeed charging. Inside the car, the clock intermittently dims and a volt gauge inside the car shows lower voltage even though a volt meter at the battery shows a good charge.
Can anyone give suggestions on where to look for the problem or what the problem could be?

 

Anything else going on? Do any other systems operate abnormally? Air conditioning? Fans? Radio? Headlights? If some major system is messed up, you'd see symptoms. If everything is acting totally normal, then you have to start hunting.

I think to get Mini R50/53-specific advice, you probably will have to provide more specifics on what the car is doing. Maybe the history too. How did you decide to replace the battery and alternator?

Anyways, I would start by visually inspecting the cables as far as they are easily accessible, looking for corrosion or other damage. Then start measuring voltage drops in easily accessible locations, like the ends of the main battery cables, and the fuse and relay boxes. So if you have 12.5 volts at the battery terminals, but 12.0 volts at the far end of the positive cable, then that cable has too much resistance. Probably a bad terminal or connection.

That's just looking for low hanging fruit -- I would not start trying to trace every wire this way. Just looking for anything easy to find, before resorting to brute force process of elimination and binary searches.

If that doesn't fix it, then you have to start working systematically. How to Stop Car Battery Drains at Popular Mechanics is a good general approach. You can pull fuses one at a time, and then check your voltage again. When you get normal voltage, or normal current draw, with one of the fuses pulled, you know the problem is in that system.

Fluke has a good general article explaining Diagnosing Voltage Drop. I'd use that to guide me. If you have the Bentley manual -- and you really should -- it has a section on general troubleshooting strategy, and specific tests for Mini systems.

 

Any problems outside of the clock dimming? Where are you taking your measurements from inside the car? Everything inside the car operates on 12V, so you're not going to see 14.6V at the cigarette lighter.

Does the car have a sunroof? Are the drains leaking? Is there signs of water ingress around the BCM in the passenger footwell?