Thanks for the responses. I think the thing about some of the older shoes (and also some racing flats) is that being low to the ground is inherently more stable than being up high, so this lets one get away with not having extra stability items (big medial posts, plastic, etc.). Also, a flexible, low to the ground shoe may let the foot and its arch function more naturally -- but it will be an individual issue whether this is a good thing. I don't think any particular flavor of shoe carries no risk of injury. But I started doing this when I was getting older (I'm 39) and noticed that "Old John" Kelley ran Boston at age 80ish in minimalistic old Tigers, and Lydiard in his book argues for wearing a minimalistic shoe which is tight and lets the arch work naturally. It was just interesting to see these viewpoints which oppose the standard advice.
As to some individual points:
To GRDC -- I think the Tiger '81 is quite good in the heel, it has a good heel counter and never slips on me and never hits my Achilles. If it hits your Achilles, you could trim the top of shoe with a razor, but I never needed to.
To BearsXC -- I think some modern shoes wear out at 500 miles because the midsole loses its bounce. These older shoes don't have much midsole or bounce; that is probably the point of them, they are closer to running barefoot. I find it forces me to run lighter and more efficiently, as crashing down on my heel when I land hurts too much to be an option in older shoes. The older shoes mainly wear out when the sole wears out, or the upper breaks. Oddly, for me the shoes that best "form to the feet" are very simple leather shoes; I don't especially hate modern shoes (I've got a lot of 'em), but the new synthetics won't mold to much.
To JasonInBangkok -- I think I might've had the same shoe in '79 (was that the Nike that looked just like the Tiger Corsair?).
To MNChris -- I have a pair of original Chariots too; I still wear them on slow or recovery days when I need a little less intimacy with the ground. But the Chariot was actually a fairly thick, plush, protective shoe when it came out and is pretty stiff relative to the minimalistic retro shoes listed above. It's only the more recent generation of shoes which make the Chariot seem minimalistic. But the Chariot is a great shoe in a lot of ways, beautiful even in its gray ugliness. For real minimalism, try the Tiger Mexico '66 or Puma Topwinner (I think I'm gonna like the Topwinner, just got a pair). It's always amazing that Ron Clark and Ryun and Keino and Bikila (when shod) must've done a lot of miles in these types of shoe.
Happy trails, EricG