TLDR version is in bold below
Since I've re-capped far too many radios I had to develop a method of real time error correction.
method 1) Divide the board in grids and replace all within a grid. Go to the parts list and cross it off.
method 2) Go to the parts list and proceed by number.
In either case do ONE at a time. Remove one at a time and replace with known good cap. There is such a thing as bad as new. Mark the top of the cap as done and check for solder bridges.
Obscure, rare, warning. Occasionally oxides will form on the leads of parts that have been on the shelf since bell bottoms and Nehru jackets. The solder will appear to form a nice blob but the only thing it's electrically connected to is the solder pad. This is especially noticeable if the leads are iron/steel rather than tinned copper. test with a magnet if unsure and pre-tin the leads.
As mentioned above , solder bridges suck to find when you have to look at the whole board.
method three is a little different. As Nomad has said repeatedly "just how long do you expect the parts and pieces of a 40 year old car to survive?" Same with a radio. On the other hand there is the if it ain't broke fix it until it is. Somewhere in between is the pick a number method. If after you have diagnosed and replaced a PS filter cap, an audio coupling cap, and maybe one or two miscellaneous caps , you might as well do the rest. If however it was just the PS filter and one or two others , leave it alone.
While you're at it learn your radio. This is easier with a PhotoFact but only marginally more difficult with a schematic. When you're replacing a cap what does it do ? Is it coupling, filtering, audio shaping, time constant or PS de-coupling?
Last but not least is the best approach for someone that doesn't do this all the time. Replace one at a time and test.
This one is the most labor intensive however there is no way you are going to have to back track and fix more than one component at a time.
This was the method I used to re cap an Icom IC-735 that had been "spiked". I took it on as a dare.
That was 80 + caps and a sandwich board that required complete disassembly of the radio. Add to this the complete rebuild of the LPF board and replacement of sundry other filters and the well known trimmer cap replacement. Now imagine this radio far enough apart to replace all the caps yet still able to turn it on and test after each one. This took about ten hours NOT including the tune and alignment.Note , I did have right angle, constant vacuum solder removal and several third hands secured to a bench along with useful single purpose jumpers.
Of no interest but to the more experienced and or self employed here (not me , I'm a hack) things like this really make you question what your time is worth. Imagine $50/hr , the radio isn't worth it. I find them around $300 to $400, This repair was near $600 and my end of it only $225.