I just changed the battery on my 98 Mazda 626 and now the battery light comes on and stays on after starting the car. I checked the battery and it's reading 12.8v with the engine off, and 13.8 with the engine on. Another time I tested it it showed 14v while running and the battery light was not on.
I also did a diode test as per Paulster's comment, and it showed 1 in one direction and -1199 in the other direction, which seems within spec.
It didn't do this with the old weak battery, or at least I didn't notice it. I just washed the engine compartment with degreaser, a brush and a water hose, but kept the battery, alternator and distributor covered - not sure if that's relevant.
EDIT April 7th, 2016
So this problem has occurred again. Everything was fine at 14.21 volt for awhile, then I went for my inspection. During the emissions part they hook up to the battery posts. As they were disconnecting, the battery light came on, but went back off after a few minutes.
Then today, I revved the engine hard, it stumbled and almost died, then the battery light came on. Got out to check and saw 13.75 volts, with a reading of between 0.02 to 0.04 volts between the negative terminal and the alternator casing.
I'm thinking maybe there is a problem with the connection to negative post, and both these events jostled it enough to cause a problem.
Here's a picture of the negative post:
I guess I'm going to try and clean the connector and maybe sand the inside of it to see if that helps.
EDIT 2: April 7th, 2016
OK, so cleaning and sanding down the inside of the connector and the post didn't help. I wonder if these two events might have caused some of electrical surge that screwed up a diode somewhere or something strange like that?
EDIT April 8th, 2016
I checked the tension on the alternator belt and it seems to be in spec. I also checked voltage between the B+ post and the negative battery terminal and it's also about 13.8.
