ORIGINAL: DMalyuta
P.S. Just how dangerous are lead acid batteries and what precautions should I take? I've done a fair bit of environmental chesmitry for exams recently, and it had scary stuff about lead and its health effects- going from stomach burns to cancer.
Don't worry about the contents of the lead acid battery UNLESS you foolishly try to cut it open. The contents won't jump out of the casing of the battery and bite you.
Lead is indeed toxic, but it has to get inside you in order to affect you. If you don't expose yourself (or others), it won't hurt you (or others). You can handle lead metal without any hazard, but you have to avoid ingesting it - for example, indoor gun ranges often have microscopic lead dust in the air that people can inhale. That's not good. BUT: your starter battery should not produce any lead dust.
The acid gel in the battery can indeed cause skin burns, but again only if it contacts your skin. Don't break open the battery.
And, when the battery is dead, take it to someplace that can recover the lead and dispose of it properly, don't just throw it in the trash.