I have had similar issues with numerous cars over the years. I have had it go both ways, bad battery and bad alternator.
The battery is used to start the car.
The alternator is used to run the car and charge the battery after the engine is running.
I know from experience that a battery with a bad cell can cause the weirdest electrical system problems and could take out an alternator. So, if you have a battery that won't hold a charge or dissipates it charge quickly, replace it.
My weirdness issue I ever had is that AutoZone tested my alternator and it passed, but at times when driving, it would not produce voltage and my car was actually be running by the battery alone. I'm not putting down AutoZone in anyway. It was an intermittent alternator issue.
So, what I had to do is carry a voltmeter in my car waiting for this occurrence to happen. If the lights would dim, I immediately pulled over and kept the car running. I then tested the voltage across the battery. It needs to be around 14.1 - 14.7. If not, you got it, bad alternator.
IMHO, you either just have an old battery or your alternator could intermittently be failing. Why do I say that? Alternator tested fine, yet your battery has a 1/4 of the CCA it should, meaning a weak battery. So, if your battery is old, than it is probably just your battery. If fairly new, than I would guess your alternator is bad or you have a bad ground.
Are you charging your battery tonight? If so, ensure it can accept a full charge and that after starting your car a several times, it doesn't loose a significant portion of its stored voltage. For example, after the charge, it's voltage should around 12.5 volts. If you start the car three times and shut it off right after it starts. After waiting a few minutes, measure your sitting battery voltage across your battery. If it has decreased below 12 volts or so, it's a bad battery.
Sorry for the long response, but I hope it helps you out.