What should I do if I make on-the-spot corrections that land on deaf ears (leaders are included)?

Some contextual information would be helpful, but I'm guessing what you're asking is this: What do you do if you make a correction, someone refuses to fix themselves, and their chain of command doesn't support you?

It's a tough situation without "top cover." I was in a similar position recently. I made an on the spot correction and an NCO outside my formation straight up blew me off. It wasn't "chickenshit" either. Said NCO was creating a safety issue and violating well known Army policies. Knowing what I do about his chain of command, his Commander would've likely told me to kick rocks. I elevated it to my BN XO instead, who said he'd handle it. Sometimes that's all you can do. I've also seen firsthand where a senior leader refused to discipline a Soldier based upon their ethnicity and gender. Essentially they were more worried about a potential EO complaint over good order and discipline. Those are the situations I write about in my green notebook, under "what I'm not going to do when I'm in charge."

At any rate it's frustrating to see leaders who fail to enforce standards. This would be my advice: If you can't elevate the issue, then remember that situation when you're in that position of leadership.

If correcting a subordinate outside your chain of command and its minor ..make it and move on. If major (cussing at spouse in the PX ) make it, note SM's CofC and have a word with leadership, one rank up.
If correcting a subordinate inside your chain of command and its minor ..make it and move on, make note to let their leadership at lowest level "marquez was not wearing his headgear between car and PX"... If major (cussing at spouse in the PX ) make it, have Sm meet you and his leadership for a talk...so both sides of the event can be heard at the same time by leadership, and move on.

If its a senior person and minor... offer the information needed to know what is being done is wrong and move on.
If it's a senior person and major deal offer the information needed to know what is being done is wrong, if they accept it move on..If they do not accept the constructive, professional, supported by reg, not just opining correction...My suggestion is bring it to YOUR chain of commands attention and ask them to handle it.

In the Air Force you get One verbal warning. If that doesn't work you get a letter of counseling (LOC), if you do it again its a letter of reprimand (LOR), if that doesn't work it is an article 15. An LOR and article 15 both effect your annual performance report and of course the article 15 is a demotion also.