How often have you seen a judgement call reversed?

We had a situation one year where we ripped a double down the line, saw chalk and the HU calls foul ball.  Our 3rd Base coach is yelling at me to appeal.  I ask the HU umpire to ask for help and he does.  BU umpires call it a fair ball because he too saw chalk and they gave us a ground rule double.

On a separate not, at least once a year we see tag plays on the 1st base line over turned due to bad angles from the BU being behind mound during sac bunt situations.

In the context you’re using “judgement”, every single call is a judgment call, and in that sense it isn’t uncommon to see calls reversed.

I played for a college summer ball coach who occasionally got calls reversed. On the bench we joked maybe the owner of our team was in charge of hiring umpires. It seemed our coach intimated umpires into changing calls.

This was before the proliferation of collegiate summer leagues and all games being umpired by NCAA umpires. Back then some where, some weren't. Our coach knew who he could intimidate.

Don't think I've ever seen it, and don't expect to.  So many coaches act like children over questionable calls, so many fans act like degenerates over questionable calls, I don't blame umps for not reversing calls.  

Quite simply, umps are doing a difficult job and they will make mistakes. The thing is, coaches and fans make far more mistakes due to their bias towards their team.  Then fans and coaches hold a grudge for an entire game over a perceived slight.  I don't really fault them for not giving either side a reason to complain about bias even more.  Imagine the hell that will break loose if one coach argues a call and an umpire overturns it.  Your just asking for chaos. 

At my son's high school, some parents will personally attack the umpire, saying that the umpire, not the call, is terrible, shouting disrespectful things to the point that the umpire has to stare over at them, passing around snapped photos that they think shows the umpire was wrong in his call.  One parent got kicked out of an away game for going off on an umpire.    I just have to walk away gritting my teeth a lot of times.

Nothing more irritating than fans who don't know the rules who are now convinced that he ump has been "paid" by the other team.  They sit their all indignant the whole game, yelling at the umpire.  

Forbid that an umpire call a batter out for leaning in on a pitch.

I see it happen sometimes on "what happened?" judgment calls: pulled foot at first base, swipe tag at first base, checked swing, fair or foul on an apparent home run.  

I've seen the base umpire jump in during live action to overrule a catch/no catch call on a third strike the plate umpire had an out and the batter started running.

I don't recall seeing a catch/no catch call on a batted ball overturned.  Good umpire communication and eye contact should prevent it from happening in most situations. For example, one time I was the base umpire in position C, and the second baseman laid out while running directly away from me on a short bloop to the outfield. His horizontal body screened my view of the catch. My partner yelled, "I got the line" even though it wasn't particularly close to the line. I made eye contact with him to acknowledge, and he took the call. That's how team work can prevent changed calls.

A couple weeks ago, at the coach's request, my partner asked for help on a call of whether a runner went more than three feet out of his baseline as he scrambled back to third when the defense threw behind him. My partner was set up in fair territory to see the tag, and called him safe because he clearly saw the tag was missed. He changed his call based on my view looking down the foul line from home plate.

It shouldn't happen on "in what sequence did things happen?" judgment calls.  Was the tag applied before the runner's foot touched the plate?  Did the throw to first beat the runner?  On those, the responsible umpire just has to make the call and own it.

It must happen with some regularity -- heck, NCAA has a whole section / appendix on what call can and can not be reversed and how to handle them.