Good engineering for Audio Amps
For learning about op-amps and their problems, I'm tempted to suggest App Note 47; it's very long and focuses more on higher speed applications, but it has a lot of practical information on debugging this kind of system. 

"How can you learn from experience if you can't identify the problem and just hope the circuit works the next time you attemt to build it?"

You have to localise the problem, even if that's just to one half of the circuit or another. You have to either build up from something known to work, or dismantle down to a definitely faulty core.

You need a model of the system, either a mental one or a simulation. Then you need to find out where the reality differs from the model. For audio stuff, this will involve poking around with an osciliscope a lot.