First thing to say is that I 'keep' everything. I never cut leads when I take a component out of circuit. That way a future owner can always put them back.
I'm very reluctant to keep either the coupling caps or the KT66 cathode cap. At best the latter dries out and becomes useless. At worst it explodes and/or shorts out. If it shorts then the KT66s turn hard on and it's pot luck as to what goes bang first (sadly it's often the mains transformer HT winding, but it could be the output transformer primary and even if they survive it won't do the KT66s any good either). Likewise the coupling caps very often go leaky (electrically). This may happen quite suddenly and without warning, so testing isn't much help. Equally it may only show up when they have hundreds of volts across them and have got properly warm. It often drives one of the KT66s into red-plating thermal runaway which again can take out the mains transformer or the output transformer.
I tend to replace the Mouldseal cap between the EF86 screen grids too. The insulation on the outside of this is prone to cracking (often so badly that big lumps fall off). Moisture gets in and the cap deteriorates. There may be no immediately audible effect (although the distortion will have risen significantly). But if either of the EF86s should start to decline then things can get a lot more exciting. The plastic insulation on the Mouldseals really stinks when it gets hot.
The resistors all creep high in value. This upsets the amp's balance. I can replace them or I can retain them (which can be worth doing if they're all original, as here) and pad them back down to their correct values with neutral metal film ones slipped in underneath them.
With care the smoothing blocks almost always reform fine. Without care (i.e. just switching the amps on after many years of disuse) they go bang irreparably, sometimes blowing the rectifier too.
I test the valves in circuit and if they're still good (they often are) I keep them, juggling them around so that small offsets in some are compensated, as far as possible, by small but opposite offsets in others. Sadly KT66s which haven't been used fairly regularly are often prone to going 'gassy'. This can be a real pain to try to deal with and treatment is by no means always successful.