Everything important has been said before. But just to repeat everything from my perspective, which is running a facility with >20 analog desks:
1. switches: see John´s post above. But if they make a popping noise while switching then they are switching DC which means the surrounding electrolytics are leaky and need to be replaced - not the switch. If switches have contact problems and have gold contacts then use pure alcohol for cleaning. If they have silvercontacts then use something like deoxit or kontakt60. Always cover the PCB with towels to avoid any liquid + metal particles litter the PCB and cause leakage current.
2. broken solder: all parts which are prone to mechanical stress can at some point have broken solderconnections. Switches, pots, faders (if soldered directly), connectors, jacks, etc. Resolder these spots.
3. trimmers: uncapsuled trimmers have dirt problems, as well as the mechanical pressure of the wiper will get less over time. This means contact problems. Replace them. Capsuled ones are less likely suffering from dirt but still age will reduce the contact pressure. Knocking helps to find out if the contact force is low.
4. pots: see above. If they are scratchy then they may have DC on the trace. Recap the electrolytics surrounding them then turn them 50x and check afterwards if the still are scratchy
5. electrolytics: dry out over time depending on age, heat and humidity. I personally tend to first recap (old) channels before I start searching for problems. In case ´lytics are the problem then it´s solved. If not then it sounds better/like new. Since there are many electrolytics in every channel there are many of them which can be the source of trouble. Measuring all of them is unpractical. As soon as they are unsoldered for measuring they can be replaced with new ones anyway. John´s advice to measure performance of a desk is a good advice though. It can oint you into the right direction.
6. tantals: I always replace them. They can go short if they die which means danger for the most circuits they are used in. Modern tants (90s and later) are way more reliable and less prone to failure than older ones.
7. IC sockets: 70s and 80s gear often had colored (red and blue) sockets which lose their contact force and create contact problems. If you see red or blue sockets replace them. Buy precision drilled sockets (they have round holes for IC legs).
8. ICs: I had one 5534 fail in a circuit all my lifetime in an unpredictable way. Otherwise they work or don´t. No TL07x or LF35x failure here ever. If you see old chips with blackened legs then the silver surface has created oxide which makes contact problems, esp. in older sockets with springcontacts.
9. ribbon wires, esp if they have selfcutting contacts or any other cble assembies with selfcutting contacs: copper + air = copperoxide = contact problems: replace
10. all the rest: there´s not much left over since 95% is described above
good luck hunting down your faults
