If its the tiny white dots your talking about they appear to be spider mited. A systemic insecticide it great but check the label, some palms can't tolerate it. By the way the Fish Tail palm has ragged edges like that, they do not appear to be eaten.
I seem to get spider mites at the drop of a leaf *U*
If you have the time, a dish cloth or piece of gauze dipped in vinigar water and and just wash them off. I try not to get the water down into the pot, but sometimes it drips in and has never seemed to hurt anything.