Previously, batteries need to be disposed properly due to content of mercury, cadmium and other heavy metals. Nowadays, battery makers have moved to remove all toxic heavy metals from the batteries. Most of the batteries nowadays, including rechargeables, no long contain heavy metals and need not have special disposal method.
One of the batteries that is still in use that require special disposal is the NiCd rechargeable battery. This battery is still needed in very high drain equipment like power tools and remote control cars.
IMO, old electronic equipment posed more problems than batteries, due to the lead content in the solders. Another item is the mercury containing fluorescent tubes.
BC