In the answer to another question, I read that it's bad to short-circuit electrolytic capacitors. Why is that? What happens if I do?
Electrolytic capacitors may become permanently damaged by excessive peak currents, which will definitely occur during short-circuit events. The reason is that (a) the internal resistance will cause a momentary, but large power dissipation (heat!) and (b) the distribution of the current spike inside the capacitor will not be formed evenly across the large area of the aluminum foil and hot spots may occur. The electrolyte may vaporize along these small zones and damage to the insulating aluminum oxide layer may occur as well.
If you're lucky, the capacitance will decrease just a bit or the top of the can may change its shape into something like a dome. If you're very unlucky, the cap may fail and heat up quite a bit (and eventually blow).
With very large currents, e.g. during inrush events into the primary caps of switching power supplies, you can actually feel how the caps heat up in an unhealthy way (don't touch live circuits or charged caps!!!). Such inrush events may be viewed as the opposite of a short circuit condition, just that the current flows in the opposite direction ("into the cap").
BTW: Also true for other capacitors like ceramics. I've seen ceramics explode, too, when they were subjected to rapid discharge events. The ceramic dielectric material changes its shape just a tiny bit when the electric field varies. If this happens fast, enough force may be created for the capacitor to blow. Disc capacitors will withstand some abuse, ceramic multilayer capacitors (MLCCs) are quite sensitive.