What direct or indirect observations of dust can one make by eye or with binoculars?
If you can see the Milky Way, then in Summer through early Autumn you should be able to see the "dark rift" which runs through the middle of the milky way from Saggitarius to Deneb in Cygnus. This is a dust band in the Milky Way.

If you live far enough South, you can see the Coalsack, a quite dense dust cloud near the Southern Cross, and also clearly visible without optics.