How do you know if a capacitor is wet?

If it was a "wet" capacitor with a gel / liquid electrolyte, that was likely either ethylene glycol (aka "anti-freeze") or boric acid (think Borax laundry soap). If it was a solid capacitor, the equivalent of an electrolyte was another film of manganese dioxide (MnO2). Wet caps usually pop, but not smoke.

What happens if a capacitor leaks out?

What you're smelling and seeing is the electrolyte that's leaked out. Depending on what the capacitor in question is actually doing, you may not see an immediate impact (as you noticed), but things will degrade, and what's worse is that the other capacitors are likely to start failing shortly.

Why do I smoke when soldering a capacitor?

If you're concerned about lung damage, the smoke that comes from the flux every time you solder something is probably what you should focus your attention on. If it was a "wet" capacitor with a gel / liquid electrolyte, that was likely either ethylene glycol (aka "anti-freeze") or boric acid (think Borax laundry soap).

How do you know if an electrolytic capacitor is failing?

There are two visible signs indicating an electrolytic capacitor is failing. These are bulging of the capacitor itself and leakage of the electrolyte. Since, this forum is frequented by people who work as repair technicians, it would be interesting to read about their experiences and whether there are other less obvious signs of electrolytic death.

What causes a capacitor to fail?

Many things can cause a capacitor to fail. Manufacturing defects, low quality components, and adverse environmental conditions can shorten the life of the capacitor. Once you see it bulging or leaking, you should consider the device failed and stop using it or you risk damaging any equipment connected to it.

What happens if you replace a capacitor?

Depending on what the capacitor in question is actually doing, you may not see an immediate impact (as you noticed), but things will degrade, and what's worse is that the other capacitors are likely to start failing shortly. You could solder in replacements, but it's probably just best to replace the power supply entirely.