The process was careful to maintain film quality since each generation of copy, back in the analog days, was worse than the original.
So the original film footage was copied and then the original was left in a vault. The copy was cut and spliced together over and over again until the editor and director were pleased with the result. Then, the time stamps were carefully noted and the original film was spliced together. And from that original, the copies for distribution were made.
To be honest, I went through this process myself with video tape but never with actual film. And I can't imagine how the audio track was handled since there has always been sound effects and audio work added to the original shoot.
The book with all the tricks for doing title for films is a real shocker. There's all the plans for building a system to hold the camera and do a "zoom" into the title. Or to have the title appear to scroll past.