Against Chekhov's Gun
Context matters. To be perfectly honest I don't know much of anything about the context to Chekhov's comments that lead to the formulation of the principle in question. I imagine he knew what he was doing.
Come right down to it I'm not strictly speaking against Chekhov's Gun. Stories should make sense. Important plot points shouldn't come out of left field. The reader/viewer should have a reasonable understanding of what the characters' options are, and Deus Ex Machina should be avoided whenever possible.
The distinction is fairly clear I think. When Batman reveals that he has lock picks hidden in his gloves that flows naturally even if it was never established previously. The reader/viewer thinks "how quintessentially Batman." They already know that he's slightly paranoid, that he tries to prepare ahead of time, that he's a skilled escape artist for whom lock picks are simple high-utility items, and that his foes' psychological hangups leave them with a predilection for deathtraps. It makes sense that he would conceal lock picks in his gloves, and given their nature and his competence it is reasonable they would remain undetected. Chekhov's Gun is unnecessary here.
The counter-example is the notorious Bat Shark Repellent. Even if shown ahead of time the idea remains mildly ridiculous. (Yes I realize it was a joke, but badly-written Batman stories frequently have him utilizing similarly overly-specific devices.) The middle ground is where Chekhov's Gun is most frequently utilized. If Batman is experimenting with a new device or technique you can bet it will be used before the story is concluded.
This leads to one of my concerns. In many cases this foreshadowing is almost redundant. (I'm going to stick to Batman as a example for the moment because he is a well-known character about whom stories have been told well and...less so.) Do we really need to be shown ahead of time Batman is working on a specific technology? After all technology and preparation are two of his primary characteristics. Would it be all that shocking if, when a problem presented itself, he went into a vault of set-aside projects and found something that could be adapted for the situation at hand? Is it out of character for Batman to have been working on personal sonar, or robotics, etc. etc.?
True this might come across as a trifle contrived or convenient, but no less so than just happening to be working on something new right before it will be needed. Moreover there are ways to soften the impact. One would be to have him find something that was not directly applicable, but close enough that it could be adapted. Another would be to show him constantly tinkering with things, thus establishing his many unfinished projects. Some might see this as wasted time, but if that was the case the tinkering could easily take place during scenes that revealed other important plot points or character details.
However I'm not certain I agree that such scenes would be wasted, which brings me to my second objection. Overly strict adherence to Chekhov's Gun destroys immersion because it is so contrary to the organic flow of real life. If every object shown, every moment documented and every character action revealed is packed tight with meaning then it is a constant reminder that this is a story. The obvious orchestration and artistry threaten to overwhelm involvement.
There are ways around this to be sure, but I do think it is sometimes worth including details or scenes that are not directly related to the characters and plot. Real life is messy. Things happen that we can't explain. People do things a certain way for no real reason, just because. Even important things can be interrupted inanely. If done well these little interludes can actually enhance a story and show other sides of the world and characters than would normally be seen. More importantly they help create the sense that these are real characters who were living their lives before and after the window in which we observed them.
Which leads to the point that brings me the most unease. Both my previous points are more about how to apply Chekhov's Gun then against it, strictly speaking. I think it is a useful principle, but perhaps it should be reassessed until we can use it more responsibly, because in some ways I think it contributes to a dangerous trend.
The degree to which much of storytelling has been reduced to mere formulas is very troubling. There are other culprits such as 'story by committee,' elevation of aesthetics/acting/etc. over story and many others. (Don't even get me started on Joseph Campbell's The Hero's Journey.) However in this environment of formulaic creation principles like that of Chekhov's Gun help make stories increasingly predictable.
This in turn leads naturally to the increasing trend of meta fiction. Because stories are predictable fans lay out their theories- at the 'water cooler' (is that even really a thing?,) online forums and in everyday conversations. This creates buzz and hype, which show creators obviously want. So they begin to go looking for it.
As the meta fiction shows go on they begin to be comprised more and more of Chekhov's Guns and Red Herrings fighting to the death for views. The narrative begins to resemble more a multiple choice test (that no one studied for) rather than a story. Events happen not because it makes sense in context but in order to provoke and intrigue the audience.
At first the readers/viewers are deeply involved, but over time they tend to become disillusioned. They may not be conscious themselves of why, but I believe it is because (perhaps subconsciously) they believed there really was a method and meaning behind everything. As they begin to realize it was all ad hoc devices for the primary purpose of drawing a dramatic reaction the illusion begins to die and the author's hand becomes visible. Eventually they lose interest.
Is this Chekhov's fault? Not at all. But like all principles his has to be used properly and responsibly. Check your story during editing, and use the principle of Chekhov's Gun to question yourself. Is everything as tight as it could be? What purpose does this scene or device serve? Don't be afraid to leave something in just because 'this is how it happened,' but don't throw in a bunch of superfluous drivel to pad the work either.
First and foremost though, start with a story. You can always clean it up afterwards, but you can't throw a bunch of formulas together and finish with a coherent whole. In the end Chekhov's Gun winds up being like guns generally. You have to practice using it safely and responsibly or it could cause irreparable damage.