What were problems with the saturn v rockets and what did the engineers do to fix it?

From what I understand, pogo oscillation was already a known problem for Saturn V rocket's first stage (and likely other stages, not sure) long before, say, Apollo 11, especially on its central out of 5 main F-1 engines due to, I guess, not sturdy enough support structure (cruciform) and the central engine's force moving it upwards, shortening the fuel line during high thrust and vice-versa when the engine was off. It might have been a known problem even before the first Saturn V flight. They (von Braun et al.) were dealing with combustion instabilities that they were trying to solve (or at least establish where the problem is) by adding a small explosive charge to the engines assembly and detonating it during hot fire testing of the first stage engines. That didn't go too well, and this pogo oscillation problem persisted at least also for the first Saturn V flight of Apollo 4.

C) the conditions in the factory have never been questioned by the employee.