Details are important; for writers, they're how you establish the nature of your world. How important they are varies depending on what you're actually creating - for genres like sf and fantasy, defining and using background details properly is a key method to flesh out the world and demonstrate how it differs from what we're familiar with on modern Earth. Otherwise, using details properly to give a feeling of the world is not so important as just getting the details right. In most literature, the setting is reality unless noted, and the details are things that can easily be verified on Wikipedia or in a travel guide.
Errors in details are, I think, something that authors should strive to avoid. Note that there's a sliding scale in this kind of error; there's a distinction from a break from reality, intentional or no, which is actually used as a point in a story - like, say, the bit in the beginning of Goldeneye where James Bond is somehow able to catch up with a plummeting plane in freefall. I'm talking more along the lines of a story or movie that claims that the capital of Canada is Toronto, with the truth or falseness of it being completely irrelevant to the story at large.
This came up recently with X-Men: First Class. I've never seen it, but on a forum I visit I encountered some grousing about a reference in the movie where the US Navy's Seventh Fleet was sent to blockade Cuba. Just some military reference thrown in for verisimilitude, water off a duck's back, right? Depends if you've actually got some military familiarity. As it happens, the Seventh Fleet is based in Japan, is responsible for the western Pacific Ocean, and this has been the case for seventy years. A blockade of Cuba would be properly handled by ships of the Fourth Fleet, which has responsibility for the Caribbean less Puerto Rico and South America.
Now, you may say that this is irrelevant - in a movie with mutants and superpowers, who gives a shit about fleets? It all goes back to reality being the touchstone for all fiction, and how that reality should be modified sparingly. There's no reason I can think of that the presence of mutants and superpowers would effect the US Navy's fleet distribution. A changed detail like that wouldn't necessarily be out of place in, say, an alternate history story, except for the fact that it's rather obscure outside its field.
No, here the answer is simple - the writers fucked up and didn't check their work. Determining the deployment zones of US Navy fleets takes less than two minutes on Wikipedia. When I'm made aware of an error like that, an error that the writers evidently didn't think to check, it makes me wonder what else they got wrong. Errors in the details fracture the willing suspension of disbelief, no matter how relevant they are to the story as a whole.