2002 Mini (non S)
Alternator went out. Replaced. Battery is brand new also.
Battery is charging properly however the clock inside randomly dims and a voltage gauge intermittently reads below 12 volts.
The battery is still charging correctly even when the volt gauge inside the car says it's not.

We've tried everything and don't know what else to look at or do. Anyone have an idea of what the issue could be?

 

Go around and check every ground connection. Maybe even if they're good and tight, take 'em loose and steel brush everything. Could be some grease or corrosion interfering.