[avmich]

> then test firing one from the batch and assuming all engines in the batch were the same as that one. This obviously isn't how things work

Curious what approach you'd propose in their place?

> The second was, as mentioned, that the control systems of the time were not that great

True. The control system was also cutting edge, and evolved together with engines, and also was much better by the 5th flight - which was scrapped - than it was at the 1st one.

[dotnet00]

>Curious what approach you'd propose in their place?

The approach used nowadays, make engines that can be fired (at least on the ground) multiple times. As far as I'm aware, all current generation American rockets can be static fired on the ground to verify that they work.

Edit: Although, come to think of it, not necessarily true with vacuum engines, but even then, they can test the turbopumps and have enough sensors to find potential issues before launching (at least once enough experience has been built up on the engine).

[avmich]

Right, but at the time to save on mass they used tricks like working with negative safety margin, that is, engines were calculated to serve particular number of seconds and performed slightly outside of elastic deformations... They did move towards multi-start engines for first stages eventually, but not during 1960-s. The original idea of using rockets was military, and those guys had hard time to understand why such a thing should work multiple times, I guess.

Vacuum engines can actually be tested on Earth, some special devices which produce external pressure decrease when the engine is running (like, if you run engine in a tube, the hot gases will push all the air from the tube making a pressure drop).