I'm pretty sure that was an anti-digital-computer kind of movie (as far as the topic is concerned, if you compare it with the historical events relevant to the space program). There aren't going to be armies of digital programmer computers in it.
not so much anti-digital as ante-digital. Mechanical turing-complete computers were a new tech and part of the story involves "obsolete" team of "human computers" getting a start on programming in FORTRAN
> Mechanical turing-complete computers were a new tech
I'm aware of that. But this was simply a matter of catching up very quickly within a changing field at the time where the new machines had already proven way superior to humans. This wasn't taking place in late 40's but in early 60's - in fact, it was taking place basically at the time when the MIT team was already designing a shoebox-sized computer to shame any human trying to control a spacecraft by hand. And as for "anti-digital", isn't a major plot point of the film an astronaut not trusting a machine's results?
More that he distrusted calculation prepared and designed by anyone other than one of the main characters.
The part where computers aren't magic and won't magically come up with correct answers despite bad input (calculation formulas in this case) was already a well established thing.
EDIT: As for well-knowness of computers - it was early enough in history of computing that Digital Equipment Corporation, despite starting with pretty much a blueprint for good computer, had to carefully ensure that it's first commercial computer didn't call itself a computer. Thus PDP series was born.
