My comments are for those that buy used equipment and want accurate sound reproduction. Sorry for exceeding 4.
1. Pick up the following books: The Art of Electronics (Horowitz and Hill), Troubleshooting Analog Circuits (Pease), Self on Audio (Self), Audio Power Amplifier Design Handbook (Self), High Power Audio Amplifier Construction (Slone).
2. Understand that the electronic components used in audio equipment regardless of how high end the equipment is have finite useful service lives. Electrolytic capacitors dry out over time, transistors become "leaky" (including "indestructible" power MOSFET's), resistors drift from their original impedance and can become noisier, etc. The service lives of components can be obtained from the manufacturers' datasheets. Excessive heat and over-voltages will seriously reduce a component's service life.
3. You may actually like the distorted sound of the deteriorated audiophile equipment. Added harmonic distortion can make impact sounds have a more forceful sound, but that sound was not what was recorded.
4. Although you will see terms like "mint", "no problems", "serviced by manufacturer", preamps and power amplifiers with ages greater than ten years will by no means be performing as well as they did when new. The seller is only giving their subjective assessment, not an objective one based on a full complement of diagnostic tests with proper test equipment. Having asked manufacturers directly, they have all said that to return their products to the same performance level when new is a costly and time consuming endeavor. Any service is designed to get the component back to a performance level commensurate with the cost you pay.
5. Even when using an oscilloscope and looking at sine waves, you have to remember you are most likely looking at the averaged waveform so it may be smoother than the actual individual waveforms. If your scope has an FFT function, seeing that display will be more revealing. The human ear is a mechanical spectrum analyzer that can be quite precise with training (see "Principles of Neural Science 4th ed." by Kandel, Schwartz, and Jessell) so you can improve your own diagnostic abilities with proper training.
6. To properly test your used equipment, a good bench 6.5 digit DVM is required. A good transistor tester that can measure leakage is also invaluable - good small signal transistors should have near 0 leakage, and power MOSFET's should have no more than .2 microamps of measured leakage - worst case .3 microamps - in my opinion. A good analog oscilloscope up to 100MHz and with an FFT function is extremely good to have. If you buy new scope, most manufacturers have all sorts of free training seminars (or low cost).
7. It is a very good learning process to take apart an expendable old amp and preamp and to test the individual components with appropriate diagnostic equipment. It will be quite revealing and make you a more "savvy" buyer of used equipment.
8. Always test replacement new components. You will be quite surprised how much variation there is with resistance values, capacitances, etc. It is especially critical to do so, because most amps and preamps require components be identically matched for optimum performance. Also, do not mix and match. If you use a component different from the original you will most likely be required to adjust voltages and will require the schematics depending on the manufacturer, you may find a level of unwillingness as they will want to protect their proprietary designs.
9. Do not mess with trimpots IMHO. From my experience they tend to have gone bad and any change in adjustment will throw things off quite a bit. Before doing so you will want to replace them with new and better versions. You will also require the manufacturer's schematics that give you proper critical voltages throughout the circuits.
10. You should be wary of "performance mods". I've seen such mods where perfectly excellent WIMA Polypropylene 160V 5% caps that have a 300,000 hour service life were replaced by SiderealKaps of unknown dielectric 200V 10% caps of unknown service life. The replacement caps were all axial and had leads in excess of 4 centimeters. The WIMA's were radial so basically had minimal lead lengths.