Most household 'dust' that falls into your tank won't make it past the surface tension of the water. With good sump circulation and good surface skimming, anything floating around in the air of your home that falls into your tank should end up in the overflow. A simple filter sponge or sock setup should take care of this sort of contaminate.
A screen top certainly wouldn't stop most airborne particles. Yes, a good skimmer will pull some of this stuff, but filter socks or such should catch it first.
I run an open top system. I just like the look... I also don't run socks or filter pads, so whatever is going in there is there, unless the skimmer is pulling it out. We have carpet, and a shih-tzu in the house. The two Great Pyrenees don't come in... if they did, it might be more of a problem

In any case, my water is crystal clear. Why? Carbon

GAC is excellent for removing lots of different contaminates, as well as the 'yellow' that builds up in our tanks over time.
Honestly, the only worries I have with an open top is (A) jumpers, and (B) aerosol cleaners, air fresheners, and such. For jumpers, all you can really do is carefully select your fish, keep the tank from getting crowded, keep aggressiveness to a minimum... and pick up the ones that jump anyway. There just isn't much else you can do. For aerosols... make sure the wife knows _not_ to use any such thing anywhere in the room where my tank is... which means I have to do most of the cleaning in this room myself. Oh well