Old caps can start to give you audible problems long before they go into a complete failure mode like opening or shorting, which would stop your amp from working. A bigger problem that nobody's been talking about is that as caps age and dry out their capacitance and/or ESR can begin to drift, and in a tuned LCR circuit, the frequency response of the circuit changes.
In addition to simple ESR testing, I perform frequency response sweeps of every amp that I work on. I've seen many an amplifier develop frequency response problems because of aged capacitors.
I use an LCR meter for ESR testing of caps. It's the right way to do things. Here's the one that I'm using. It's a "cheap" hand-held unit that costs $300. http://www.bkprecision.com/products/...-with-esr.html
The price for this kind of testing equipment is significant. Many techs that I know don't bother to own ESR meters, because sometimes relying on them can lead to a false sense of economy.
Time and heat are a cap's worst enemy. Most caps are cheap. The big ones in your power supply aren't all that expensive, and the little ones on the amplifier circuit boards are almost insignificantly cheap. Compare that to the cost of a tech's time (or your time inside of the amp) and the math says that when you've got an old amp opened up for a cap job, it makes sense to replace all of the caps that are in there at once, so that you can avoid spending another $75 bench fee (or several hours of your time) in the not too distant future to replace that old 25-cent cap that you were too cheap to replace because it tested good on the ESR meter.