The most critical parts when recapping

Thank you both for great input! This really cleared it up for me. 
About diodes:
Do you also here look for the same "values"? Or are there aspects to them that you can change?

Luckily, in my project now, I actually have replaced the large power caps, and a set of four around them. There are a bunch of tiny caps, like 10uf 50v. Worth swapping out?

As far as I can tell everything everywhere makes a difference. When you ask about is it worth it though, hard to say. Mostly because with caps there seems to be no upper ceiling on cost. Plus there's little tricks like using better large value power supply caps and then adding one really crazy good one of smaller value on as a filter cap that doesn't really affect the power supply except to greatly smooth the last tiny remaining vestiges of ripple. 
 
With diodes I would stick with whatever's in there. With diodes, if I got it right, its all about volts and watts. Watts being the heat dissipation part. What you're really doing with both caps and diodes is finding faster ones. With caps they don't really have a way of measuring but with diodes since they cut on and off they can measure switching speed and graph it and so you're looking for the one with the steepest fastest response and also the smoothest noise-free response. Because switches, which is what diodes are, tend to spike. You want fast but no spike.

You find a really fast smooth diode, that's your huckleberry.

There are a bunch of tiny caps, like 10uf 50v. Worth swapping out?

Yes, any electrolytic on the power supply rails is worth swapping out to prevent them from shorting down the road.  I used to use Panasonic FM for these, since they were reasonably affordable and had low inductance, and therefore high noise blocking.

There are a bunch of tiny caps, like 10uf 50v. Worth swapping out?

If you have the time and skill, replace all Electrolytic Capacitors, they 'age'!
Relays on amplifier protection circuits also caused problems went they get old.