Well that's an easy one for me.... and I am extremely blessed to have dedicated, capable folks serving with me.

If they don't do it OR if they don't do it right, we release them.

That would be harder on the ward level.

Come on guys... let's remember we're still brothers and sisters with them... even if we do get under each other's skin and bug the snot out of each other from time to time... so, I propose we just refer to it as "over across the river..." 

Back to the question originally put forward "how do you actually get those with whom you serve to actually do their callings?"  Well, I'm no local leader, nor do I play one on TV, but I think there are a few fundamental things that help.  Bear in mind, this is all just my opinion.  Your mileage may vary, particularly if you hold the mantle of leadership.

1.  Fit.  I hope that a Bishop or Stake President does sufficient due diligence in making sure the calling fits the individual's current capacity for service before taking it to the Lord or later extending the call after praying and receiving the confirmation.  Nothing wrong with some stretch, but it is rare success will come from extending a call to someone as organist if they don't even know how to read music (I know extreme example, but you get the point hopefully).
2.  Willingness.  How willing is the person to make the sacrifice necessary to magnify the calling?  Do they serve because they love the Lord, they love their fellow members, they enjoy the assignments, or because they feel they have to?  Or some combination of all the above?
3.  Training and practical sustaining.  We raise our hands to sustain one another when a person is presented before the respective body of saints in a given calling.  But, how comfortable is anyone when they end up just getting a notebook or a box of stuff shoved at them by the person who previously held the calling, and that becomes the extent of their training / preparation for performance of a calling?

I don't think this "here's the book, good luck" sort of things happens much in a Bishopric or Stake Presidency or High Council or maybe some of the main auxilliary heads who report directly to either the Bishop or Stake President.  These kinds of "quorums" mentor one another, help the new guy learn the ropes so to speak.  But, I would guess it happens more often than not in the less central callings.  I have experienced it in nearly every calling I've had since my mission (outside of assistant ward clerk and stake auditor).

For example, it has happened in every Scouting related calling I've had.  I love the Scouting program and serving with the Scouts too, but it scares me to death as 11 year old Scout leader that the practical level of support I get from parents, the primary presidency, the bishopric, and even the YM's portion of Scouting is the expectation that the boys will be close to or have their 1st Class by the time their year is up and they turn 12 and enter the Deacon's Quorum.  I feel this is very impractical, because I know what is at stake here.  I'm to prepare these boys to now listen to each other as leaders as well as respect an adult advisor.  I'm to instill in them a deep love of Scouting so that their Scout spirit isn't just a thing that lasts until they get their Eagle at or close to age 14 (a defacto goal -- the earn the Eagle as soon as can since we'll lose them later on -- I have clearly stated I feel misses the mark about what the whole program is about... a boy who earns his Eagle later typically is mature enough to appreciate it more at the time and later in life because he has had to overcome the outside distractions of being a teen in order to earn it... note the word "earn"... Eagle should never just be considered an accomplishment that is a just the next thing on a checklist).

Anyway, sorry I'm digressing from the example.  In order to do both the expected mandate of rank advancement as well as the more intangible seeding of a love of Scouting, I am allowed to meet with the boys twice a month for an hour or hour and a half.  I am given no assistance as in any skill instructors.  Guess it is figured that since I am "Trained" as far as BSA is concerned and gung-ho about the Scouting ritual and patrol method and that I earned Eagle, that is all that is needed.  At least there is always some other adult within voice range of us when we're meeting so we get compliancy with the two-deep requirement.  But, the point is, and I'm not faulting the folks in my ward, because just like me, they're imperfect and we're doing the best we can under the situation and restrictions of the chartering organization, I never feel like I can magnify my calling because of always feeling like I'm on my own.  It is hard to be both the first example of a one on one advisor / mentor to these boys as well as skill teacher when I don't have the tools or help or adequate time provided to do it.  We're commanded in the D&C that every man should learn his duty.  Learn his duty, learn how to do what the role entails... not have to figure it out on his own.

Is there more we can do as fellow members and as leaders in an organization, to make sure folks have what they need to be successful in doing their duty?  We're not islands.