First inspect the battery for any noticeable signs of degradation, rust, battery acid, etc. If the battery seems reasonably clean, stick it to your tongue. You will feel a slight jolt and metallic taste. You'll probably need to calibrate your tongue by testing a fresh battery and a dead battery to get an idea of what to expect.
Luckily my friend SHIFT! was around today to demonstrate. Notice his pained facial expression in the first image, this is definitely a new battery. In the second image he seems unfazed, this battery should disposed of.