If we use cotton, straw, or sheep's wool to insulate homes, can we use compressed dust? (cheap and easy to collect...)

Good insulators comprise much gas (like air) and little solid materials, because solids conduce heat more. Dust would be less favourable. Though, you might perhaps compensate that by thicker wall, provided the net result is cheaper.

To add to what Enthalpy said, it's the pockets of dead air that gives the good insulation in such systems — no convection and little conduction.

I think I could have insulated my whole block with the dust and pet hair I get from my vacuum cleaner. Dyson should come out with a machine you can just reverse and blow into your attic and walls.

 

Of course, you'd never be able to sell your home to someone with pet allergies....

If you did this in a woodworking shop you would have reinvented MDF.