Aside from historical fact, I can’t stand movies that make gross errors regarding weapons, technology, tactics, etc. Not only-fanatics-would-know errors, but simple errors that could have been corrected had someone given a rat’s ass, but no one did.
My basic criterion for this is if I can imagine the director saying to someone, “Just shoot it as is. No one will know the difference anyway.”
For example, take Die Hard 2, the one in the airport. The whole plot was based on these airplanes being stuck over an airport because they couldn’t land because terrorists controlled the airport. And there was no way to talk to the airplanes except through the control tower, which the terrorists controlled.
Of course, airplanes have enough fuel to divert to another airport in case their destination is shut down - and most people know this. Of course, airplanes have radios that can communicate with many people other than the control tower - and most people know this. Of course, all the other airplanes in the sky or parked on the ground could talk to them - and most people know this. But the directors of the movie just didn’t care. They thought the audience was too stupid to notice. That pisses me off. I can forgive the fact that they showed ejection seats in a Hercules, which doesn’t have them, because that’s the kind of fact only true fanboys would know. I can forgive them showing a hero jumping off the wing of a 747 about to take off, and surviving, even though he’d be making the equivalent of a three-story jump going 150 mph, because it was a trivial detail for an exciting shot. But when they get the easy stuff wrong, and for no reason other than laziness, it pisses me off.
On the other hand, a movie that takes great pains to get the details right develops an air of realism that makes the story more immersive and really gives you a sense that, “yes, that’s the way it could have happened.” That enhances a movie. For instance, the movie Thief depicted a sophisticated bank robber. The producers hired actual ex-cons as technical advisors, and they filmed James Caan actually breaking into safes, using the ex-cons own safecracking hardware. When one of the crooks is testing for phone lines, the correct voltages were shown on his meters when he found one. When the main character stormed a house with a handgun, he did it after being coached by Jeff Cooper, a world reknowned authority on handgun combat, on the right technique for clearing a room.
This attention to accuracy casts a wider swath than you’d think. Everyone’s an expert on something. If a movie gets a little detail right for you, you believe the others, even if you don’t know if they’re accurate or not. And it makes the movie more enjoyable to watch.