Not having your crew do things they would perceive as morally reprehensible is a fantastic start. Aside from that, providing an environment where they can disclose and/or discuss their issues with you would also work well.
Any other measures of "putting a stop to it" will only make it worse.
As an older worker, I'd say the mistrust issues of younger workers are entirely justified. If that is a problem, corporate management is hoist on its own petard.
If you wanted Gen Y to trust you, you should have treated Gen X better--or at least hidden the mistreatment better.
As for the entitlement, that's probably on their Boomer parents/grandparents. You could shove them down and kick them in the teeth until they become bitter and jaded, just like Gen X. But then you're back to the trust thing again.
So if I may humbly suggest, start treating your older workers better. First, have some to treat better. Then, give them back all the crap that Boomers once enjoyed, but which later got stripped from standard employment arrangements, like actual vacation weeks and sick days, longer-term employment contracts, career ladders without important rungs missing, viable retirement plans, job security, etc.
The younger workers were born into the networked world. They rely on friends and family to judge your company's reputation. And the source of that reputation is largely going to be people that worked for you in the past. Those older people have all been screwed by their employers in one way or another. Kids are usually naive, ignorant, and inexperienced, but they aren't stupid. They see what happens to uncles and cousins and friends of their parents.
Sadly, there's not much an individual manager can do about any of it. Those young workers are coming in expecting to get stabbed in the back, and one day, your CEO or Head of HR will call a meeting and issue you your knife--or maybe your axe. Those kids know it's coming; they have seen it happen over and over again to other people. So maybe validate the mistrust, and admit that the company doesn't care about them. Let them know that the one and only way to keep a job is to be productive enough to pay their own wage, and then some, and that everyone should plan to eventually jump ship near a port, before the captain gets the chance to throw them overboard in the middle of a crossing. Recognize that a mercenary attitude puts self first. That makes the manager's job harder, of course. Why should a mercenary work any harder than necessary to earn the paycheck?
I would (as a non-manager) use discretionary cash bonuses to reward good employee behavior, with intermittent reinforcement. Cultivate trust in you, personally, rather than trust in the company. Punishments and the threat of termination simply won't work. Just put everyone on a secret carrot schedule, and when it comes time for the next reward, set up a plausible reason to hand it over.
Trivial fun OT fact: a petard is an archaic word to describe a bomb or similar explosive device, so it would make more sense to write "hoist by its own petard", i.e. blown into the air by its own bomb.
I like to check on the kind of social circle they maintain. Loners generally don't get what it takes for a group to come to consensus about the grey stuff.
Don't handle them. Regardless of age. Pick out the worst and get rid of them. You may find the troubles with the others diminish.
Being fired once or twice in life is a character building experience. It often makes you re-assess your worth and take work more seriously. And later, as a person becomes (potentially) a manager, they realize the ego crush that is being fired and treat with respect, unlike "kid" managers who haven't been through the process and fire without understanding, sometimes for little more than an ego boost.
Also, removing impediments to the common goal is necessary for an organization to thrive.
Everyone eventually has to grow up. But it's a confusing world right now. There isn't anything to trust because we know so much more. And the school system has been preaching unrealistic pablum which gets under the skin after a bit.
Sometimes it takes a hard knock or two to understand the underlying nature of commerce and human interaction. Unfortunately, (like germophobe moms) we have made a bad habit of deferring these essential lessons thus weakening the ability to deal with the very real, very dirty world.
So for those two reasons, don't feel bad, don't try to fix and don't coddle. It won't work anyway.
Not sure were that was stated (or even implied) but since you ask, no, particularly with the modifier "anything other than".
We are born in blood. And we return to mud. That's the essence of our beginning and our end. Nobody likes this. So, we sanitize with (very important) abstractions. To make it so life is more than a reptilian struggle. To allow civilization, working collaboratively, a degree of security, care for the weak, all the things that make it possible to transcend the law of jungle and live beyond our biology. But the underlying reality doesn't go away just because we have abstracted on top of it. People sometimes forget why abstractions are important. Or, sometimes they forget there is a hard reality underlying.
The nature of the abstraction named "commerce" and the nature of the abstraction named "human interaction" is that of give and take. Not give and give. And both abstractions depend for existence on trust, on integrity, on honor, and on the willingness to part with something in exchange for something.
Point being, sometimes it takes getting down to primal gut level emotions to understand abstractions are abstractions, why they exist and how they relate to underlying reality.
Along with integrity and self sacrifice, respect is an important virtue that seems to be increasingly lacking. It won't be for long. These things will come back again because they are vital to any useful abstraction layer.
