Why have capacitors improved so much over the years?

Where are they used?

Did you verify values?

Please detail evaluation.

Please note that you appear to be a dealer of some sort:
"As a dealer I do realize the challenge it presents when you attempt to set up a high end system in a store environment. That is why our high end reference system is actually set up in a home environment." in  Audiogon Discussion Forum

For high voltages, 300 and higher including 1000 or more, I feel safer using polypropylene to electrolytic because of shelf life issues the former do not have and you can get polypropylene good for 1300 Volts for about the same price you would have to pay for banks of electrolytic capacitors wired in series and parallel to get rated 1800 Volts. The former are larger, 3" diameter but you can get an aluminum box 17" by 17" that will have enough room for two power supplied with chokes on the negative sides. I use fast solid state diodes with center taps on power supply transformers rather then risk the problems with high maintenance mercury vapor diodes and the isolation transformers for their cathodes that have to be pre-heated and could short circuit.

From the early eighties until the early nineties the transparency of audiophile-quality gear improved enormously.  This is almost certainly the improvement in passive part quality (mainly capacitors, but also to a degree in resistors.)  My observation is that J. Peter Moncrieffe in his publications and promotion of WonderCaps made believers out of many who had heretofore scoffed at the notion that these passive devices had a "sound".  Electrical engineering courses, of course, had not even considered these subjects.  I know for a fact that the folks that developed the HK Citations found part swapping a critical part of their development, at a time when virtually no one else was doing it.

Lou, what a well articulated post! Some of your quotes are priceless!

Yes, Lou's post was very good & made for some interesting reading. I can't understand either why manufacturers go through all the trouble of designing a piece of gear & then at the most critical point insert cheap caps.