A lot of it was trial and error, I've read that the Pogoing on the fortunately unmanned test flight was caused by resonance in the flexible fuel lines used. This hadn't occurred during ground testing. Eventually they figured out that the fuel lines were becoming coated with ice during the ground test but as the air was less moist at altitude the pipes were free to flap about! They fitted solid lines after that was discovered.
I think they also had an engine cut out problem where sensors shut down a good engine because they'd cross wired the the looms. After this they made the looms to each engine a different length so it couldn't happen again!