It is the overcharging and resulting out-gassing of explosive vapors you need to be wary of. I've seen it too many times to want to count. All you need is an ignition source of any kind, and you may end up wearing the case and acid present. I'm speaking from practical experience of having owned and run a foreign car shop for over ten years with all the best Snap-On diagnostic tools for charging systems.
Protect your eyes, face and any exposed skin from potential worst case possibilities with gloves, safety glasses and long sleeved shirt.
Diagnostically speaking I agree with a couple of possibilities: open sense circuit, another faulty regulator*, (*my personal favorite, can you say outsourcing to third world?), or a bad ground to your chassis, (read cooked internally, cable), from either the battery or the alternator/V.reg.
You could, to keep your current battery from completely self-destructing, add some water to each cell to the full line, but again I would exercise extreme caution if you choose to do so.