It goes without saying that you want to feed good hay, with little or no dust.
That's a given.
But it's rare to find totally 100% dust-free hay, simply because of the process of how hay grows and is baled.
It's vegetation growing in dirt! Dry dirt is dust.
It gets dustier if there has been a rain within a few days before bailing.
It gets moldy if it rains just before and is too damp or got rained on after it was cut and lay in the field and was then baled.
I can smell mold and mildew a mile away, I am allergic to it.
But even if I wasn't, mold and mildew shows up in other ways, no pun intended.
  If you pick up a flake or two of hay and it's heavier than the others, chances are it has mold in it.
Sniff, (From an arm's distance if you're like me).
If it smells musty, open it up and look.
Mold is obvious and so is mildew.
If it's even slightly iffy, don't feed it.
Better safe than sorry.
If hay has a significant amount of dust in it and does not smell musty or moldy, you can choose to soak it, hose it down, or return it.
If it's just a light amount of dust, shake it out and wet it down.
In a perfect world, all hay would be dust-free.
This isn't a perfect world.
If it were, all hay would be cut a week or so after a good rain; it would lay row after row curing in a sunny field for days before being baled.
And it would smell like fresh green grass.