Personally I find this idea scarier than a battery exploding, I am not trained with electrics (I'm a mechanical and hydraulic engineer by trade) and therefore sticking the probes from a multimeter anywhere I consider to be a little irresposible.
A multimeter doesn't supply electricity, and you don't stick them just anywhere. A battery should be periodically checked when it's removed from the charger to detect if it's under or overcharging. It's a measure of it's general condition. Better to know if your charger is malfunctioning or if your battery is not fully charging. It ain't rocket surgery. You stick the probes on the pos. & neg. terminals. If you get it backwards, nothing will happen, except the meter will probably indicate reversed polarity. This is DC current, not a 240V mains. Even if it was, meters are fused. They won't allow you to be electrocuted even if you were dumb enough to create a short across the terminals. Probe your wall outlet. Do it backwards. What happens? Nothing at all. You should periodically check the output of the charger by the same method. Compare it to the voltage it's supposed to supply to the battery. There's a good chance that this ego was using a charger that was defective. It could have been supplying too much voltage to the battery. If that was the case, it could have been detected. Those ego chargers are notoriously cheap and the first suspect in these cases.
Lithium batteries are in so many things that we trust, mobile phones, camera's, even my sons satuaration monitor has a lithium battery pack, there may have been a fault anywhere, not neccessarliy with the battery itself, a faulty charger or a slight power surge (we had one that blew the element in the kettle but was not strong enough to trip the electrics for the entire house), by this method of thinking should we spend half our lives checking these, then what about the batteries that are actually in the multimeter (I know enough to know they have batteries)?
No, those batteries have internal charging circuits that are far more reliable than what's in an e-cig, if anything is at all. The are not like a bare cylindrical battery either. A bare battery may have a protection circuit inside it, but typically, it's a cheap ten-cent PCB and if it was defective, you'd never know it until something happened, like an overcharge or over-discharge. IMRs don't have a protection circuit at all. Most multimeters run on little alkaline batteries. They don't hold the potential to explode or vent like a lithium battery does.
I have never heard of anyone being electrocuted or starting a fire, or otherwise being harmed by sticking the probes of a multimeter somewhere. If you really wanted to, I guess you could lay a probe across both terminals of something and short it out, if they were close enough together. Good luck trying that on a cylindrical battery. If you do it, you deserve to be shocked. More than once in fact. It would be good therapy for you.
