I never really liked Chekhov's Gun, as it tends to make the world feel artificial and barren. Details unrelated to the story at hand make the world feel much more vibrant and interesting. It gets worse as a story's length increases - for instance TV shows that go on for years where the main characters only seem to have relationships with 5-6 other people in the entire world.
Of course there's a separate issue where a fictional work will artificially emphasize the importance of something and then ignore it. For example, people say something's impossible, then there's a close up shot of someone's face, he slowly says "It's not...I know a guy" and loud dramatic music starts playing. There, the creators are telling the audience that this is something important, and it will be odd if it's not followed through (though even then, I've seen some creators not follow through in interesting ways).