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This is a mith that I read several times; while it is true that the safety standards weren't those of today and the Apollo missions faced countless problems, "a few mm away from catastrophe" is a bit exaggerated statement regarding the Saturn V launches, IMHO.
Well, for example, during Apollo 13, the center engine of the S-II vibrated so strongly because of excessive POGO, that its massive thrust bearing flexed 5.2 inches by 34G vibrations. It was actually calculated that, would the engine not have shutdown earlier, it would have destroyed the launcher. Luckily, the oscillations in the propellant lines grew so strong that they triggered a low-pressure switch designed to prevent the engine pumps running dry by a tank leak before structural damage occurred.
http://www.vibrationdata.com/Newsletters/October2008_NL.pdf
Because the mission had some lot of bad luck, it was really not considered that important, but for people deeper involved in the program, it was actually much more dangerous for future missions than the oxygen tank explosion.
Literally any mission of the Apollo program until Skylab had some more or less serious flaws, that often like for the Space Shuttle later only lucky coincidences prevented worse. Compare this episode of pogo for example to Gemini, where the milder pogo oscillations of the Titan 2 had been reason enough to delay the first launch until the vibrations had been low enough that a human astronaut could work in the capsule (for the performance of the ICBM, the pogo was never a problem)
If I recall correctly, the S-IVB engine on Apollo 6 performed poorly during the first burn and completely fails the in-orbit restart, forcing to use the Apollo SPS to raise the orbit.
Apollo 6 also had been the first launch to show significant pogo.
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