Blown capacitors are nice and obvious.

Most capacitors you'll find are cylindrical, with a flat side of the cylinder pointed up. They'll usually have a big X cut into that top side, allowing it to flex a bit. But if that top side is bulging a lot, that's a warning sign, if it bulged so much that it opened up and it either looks burned on top, or some kind of paste is actually seeping out, then that thing is way past done.

With capacitors a visual inspection is really all you need. You'd actually need more expensive specialized equipment than a standard multimeter to actually test their capacitance. But if you look at it, and your description might include words like "exploded" or "popped", or "wtf is this mess?", then it's bad.