Outside these two conditions, the only other thing is age, other than that, they tend to not explode.
source: https://www.vishay.com/docs/49268/tn0003.pdf other source: at $WORK we are having some problems with igniting tantal caps
A short dumps a pile of current across the capacitor. an open circuit usually just means your circuit doesn't work well.
Don't use tantalum without a careful plan to deal with this issue... why are you forced to use them instead of a modern electrolytic?
The reason is a mismanaged project. Power budget on a CR2032 is tight and initially a supercap with much bigger capacity was planned. The company producing those went out of business and people were forced to somehow get it to market, working. We did, but now those new tantal cap problems arrived.
I turn around and see my two class mates looking shocked and confused, covered in fine fur all over their upper bodies, along with the desk.
Never got around to understanding just how they managed it, but they most certainly did manage to blow up that capacitor in a spectacular way.
While they look fairly harmless, one should also never forget that capacitors are the most dangerous part of any electric circuit; they don't become safe if power is off and they have no limit to their current other than "what the wire can do", which is usually northwards of "the wire evaporates".
I've experienced various caps burn their legs and solderpoints in less than a millisecond without warning once a short was realized. And on top of that, the huge currents running through wires not intended for that will usually cause quite a bit of inductive backlash in nearby components.
I'm pretty much convinced this was not a mistake, it was a "Be really CAREFUL with this stuff!" object lesson.
Purposefully weakening the container can bring this sort of behavior out at lower levels.
Gasoline is flammable, but it needs the right fuel air mixture to actually explode. Car fires are relatively common, but as far as I know car explosions are not.
So, yes, they can explode. That's actually pretty much the point.
(I do not believe this will actually be a primary impediment to adoption of either Lithium Ion or Super Capacitors)