do you have an udp on the alt? If it is not the stock size then you could be under-charging the battery. The alt is probibly working fine, but not putting back as much energy into the battery as the car is taking out, thus slowly killing your battery. Also, cold weather will kill a good battery, I know from personal experience.
Did you have any lights come on in the cluster? When my alternator started to go the battery light would iluminate when I was at idle at red lights. As soon as I would rev the engine the battery light would go out. As soon as the rpms would drop back to idle the battery light would come on.
When you started it later that night and noticed the lights were dim, you said you "gave it gas and everything seemed ok". When you reved the engine, did the lights, cluster, whatever was on get brighter? Did it go dimmer when you released the throttle? Did the lights stay bright for a little then go dim?
