Similarly, the "oh we forgot the moon rocks!" bit was actually the engineers realizing it ahead of time and changing the prep checklist to account for it, rather than a last second dash. This was only because there were so many engineers, and they had made themselves so immersed in the task, and they had such good lines of communication that someone identified the problem and was able to escalate the fix to the correct levels at the appropriate time. This didn't happen by accident, but was the result of years of working together, both training and the experience of actual flights that made these teams so good.
Separately, there were a few things the movie got wrong just as one-off moments. At launch the arms retracted simultaneously, rather than sequentially as shown in the movie (not quite as cool looking) and if you listen to the bit where Lovell says "Houston, check my math here" he is doing addition, which can't be done on a slide rule.