"if you are looking for a podcast that carefully examines the evolution of D&D's rules,"
If I was looking for something like this, is there something anyone could recommend?
Thanks
(I'm more interested in the story in When We Were..., which is really really good so far, but when that's finished I might be interested in moving on to the history of the game itself.)
I don't think there's a podcast which does this, though I'd be happy to hear otherwise.
If you're up for a book,
Playing at the World is the most complete and authoritative work on the evolution of D&D from all its myriad influences and precursors. It's about ten years old now, though (which means some info is missing which has since come to light), and can be expensive on the secondary market. Good news is that it's being reprinted in a revised edition, in two volumes, and the first volume came out this year (from MIT Press).
Peterson's more recent
The Elusive Shift is shorter and should be easy to find, and it chronicles and analyzes what happened after D&D got published, as players and designers made OTHER RPGs and debated what RPGs were capable of and best for.
The same author's
Game Wizards is about the business side, from before TSR was founded until Gary left in the mid 80s.
PatW doesn't go much beyond Original D&D, though, so if what you're really looking for is discussion of how the game mechanics have changed through its various versions and editions in the past 50 years, I don't know it there's any one good source for that. The panel discussions of the editions Mr. Fahey just mentioned are pretty good, but they are a bit informal and loose. Delta's D&D Hotspot, a venerable OSR blog, has an intermittent series of articles titled "[subject]
Through the Ages" which examines various parts of the rules and how they've changed over the editions. Often it's a deep dive into a particular spell, but sometimes it's a broader topic like how healing works, or aging.