Has anybody ever had a moment where you should've put a subordinate or superior in check, and missed the opportunity to do so.

I had a moment when I attempted to disagree - ever so tactfully - with my immediate superior, and it failed miserably. I attempted to state my opinion, an opinion which was not in agreement with my boss's opinion. Now, I had been working in the field in question for 30-plus years, and my boss had never worked in the field ... But it ended in a "one-way conversation" and I was on the receiving end of it all. Even as a civilian I learned that some military officers are so full of themselves, that they cannot be disagreed with.

To directly answer the question, of course, for multiple reasons.

No one likes to be corrected and personally, I get extremely defensive when I am corrected in public, regardless if I am right or wrong! Of course, as a disciplined Soldier, if a superior corrects me this way, I bite my tongue, accept the correction, then move on. (I may address it in private depending on my relationship with the individual and how important it is to me.)
Understanding this, I know that it is better to praise in public, and correct in private, however, we all know there are times, when we know someone is speaking incorrectly. If it is important enough that a correction is necessary (wrong info that will negatively impact) then a tactful correction is necessary.
I have been accused of being too negative and critical (I consider it critical thinking!), so am very aware of how that comes across, especially with subordinates, and try not to make it a big deal when I do correct.
I am also extremely hard on myself, so if I don't make a correction where one should have been made, I do often replay that in my head, looking for ways to do it differenly next time.
Of course my most favorite corrections are to superiors, when I know they are wrong, but having to find the best way to tactfully correct them! Sometimes I am successful, othertimes, not so much.

Not sure how you mean, I would never step up to my seniors in "check", not due to dear but due to the military hierarchy, these things take care of themselves sooner or later, being told by a Jr NCO or Office they are doing something wrong is a recipe for disaster, at least in my day, it would never come to mind to do so.
As far as a subordinate, most certainly.